List of Publications - Lutz Recke
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[1]
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L. Recke.
An example of bifurcation of solutions to the basic equations for
carrier distributions in semiconductors.
Z. Angew. Math. Mech. (ZAMM), 67(6):269-272, 1987.
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[2]
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L. Recke.
On linear stability of bifurcating equilibria.
Math. Nachr., 140:59-68, 1989.
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[3]
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L. Recke.
Stability of bifurcating solutions of equivariant equations.
Nonlinear Anal., Theory Methods Appl., 23(8):971-997, 1994.
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[4]
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L. Recke.
Applications of the implicit function theorem to quasilinear elliptic
boundary value problems with non-smooth data.
Commun. Partial Differ. Equations, 20(9/10):1457-1479, 1995.
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[5]
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D. Peterhof, L. Recke and B. Sandstede.
On frequency locking of self-pulsating two-section DFB lasers.
In In Self-Organization in Activator-Inhibitor-Systems: Semiconductors,
Gas-Discharge and Chemical Active Media ed. by
H. Engel, F.-J. Niederhorstheide,
H.-G. Purwins and E. Schöll,
Wissenschaft & Technik Verlag, 1996.
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[6]
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U. Bandelow, L. Recke and B. Sandstede.
Frequency regions for forced locking of self-pulsating multi-section
DFB lasers.
Preprint 345, Weierstraß-Institut für Angewandte Analysis und Stochastik Berlin, 1996.
Optics Communications, 147:212-218, 1998.
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[7]
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L. Recke and D. Peterhof.
Abstract forced symmetry breaking and forced frequency locking of
modulated waves.
Preprint 256/257, Weierstraß-Institut für Angewandte Analysis und Stochastik Berlin, 1996.
J. Differ. Equations, 144(2):233-262, 1998.
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[8]
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L. Recke.
Forced frequency locking of rotating waves.
Dedicated to A.M. Samoilenko on the occasion of his sixtieth birthday.
Ukrainian Math. J., 50:94-101, 1998.
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[9]
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L. Recke, K. R. Schneider and V. V. Strygin.
Spectral properties of coupled wave equations.
Preprint 362, Weierstraß-Institut für Angewandte Analysis und Stochastik Berlin, 1997.
Z. Angew. Math. Phys. (ZAMP), 50:925-933, 1999.
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[10]
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L. Recke.
Applications of a new G-invariant Implicit Function Theorem.
In Proceedings of the EQUADIFF 99,
ed. by B. Fiedler, K. Gröger, and J. Sprekels,
volume 1, pages 204-206, 2000.
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[11]
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J. A. Griepentrog and L. Recke.
Linear elliptic boundary value problems with non-smooth data: Normal
solvability on Sobolev-Campanato spaces.
Preprint 446, Weierstraß-Institut für Angewandte Analysis und Stochastik Berlin, 1998.
Math. Nachr., 225:39-84, 2001.
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[12]
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K. Gröger and L. Recke.
Preduals of Campanato spaces and Sobolev-Campanato spaces.
Math. Bohem., 126:403-410, 2001.
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[13]
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K. Gröger and L. Recke.
Preduals of Campanato spaces and Sobolev-Campanato spaces: A
general construction.
Preprint 498, Weierstraß-Institut für Angewandte Analysis und Stochastik Berlin, 1999.
Math. Nachr., 230:45-72, 2001.
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[14]
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M. Kucera, L. Recke and J. Eisner.
Smooth bifurcation for variational inequalities and reaction
diffusion systems.
In Proceedings of the 3rd International ISAAC Conference,
Berlin, 2001, pages 1125-1133. World Scientific Publishing 2003.
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[15]
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F. Jochmann and L. Recke.
Well-posedness of an initial boundary value problem arising in laser
dynamics.
Preprint 515, Weierstraß-Institut für Angewandte Analysis und Stochastik Berlin, 1999.
Math. Models Methods Appl. Sci., 12(4):593-606, 2002.
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[16]
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J. Eisner, M. Kucera and L. Recke.
Smooth continuation of solutions and eigenvalues for variational
inequalities based on the implicit function theorem.
J. Math. Anal. Appl., 274:159-180, 2002.
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[17]
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L. Recke, J. Eisner and M. Kucera.
Smooth bifurcation for variational inequalities based on the implicit
function theorem.
J. Math. Anal. Appl., 275:615-641, 2002.
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[18]
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L. Recke, J. Eisner and M. Kucera.
Smooth dependence on parameters of solutions and contact regions for
an obstacle problem.
J. Math. Anal. Appl., 288:462-480, 2003.
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[19]
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J. Sieber, L. Recke and K. R. Schneider.
Dynamics of multisection semiconductor lasers.
J. Math. Sci., 124(5):5298-5309, 2004.
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[20]
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S. Yanchuk, K. R. Schneider and L. Recke.
Dynamics of two mutually coupled semiconductor lasers: Instantaneous
coupling limit.
Preprint 879, Weierstraß-Institut für Angewandte Analysis und Stochastik Berlin, 2003.
Phys. Rev. E, 69(056221):1-12, 2004.
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[21]
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J. Eisner, M. Kucera and L. Recke.
Smooth bifurcation for an obstacle problem.
Differ. Integral Equat., 18(2):121-140, 2004.
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[22]
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J. Eisner, M. Kucera and L. Recke.
Smooth continuation for a model of unilaterally supported beam.
In Proceedings of an International Conference on Mathematical and
Computer Modelling in Science and Engeneering in honour of the 80th birthday of K. Rektorys,
pages 108-112, Prague 2003.
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[23]
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S. Yanchuk, K. R. Schneider and L. Recke.
Dynamics of two f2f coupled lasers: instantaneous coupling limit.
In Proceedings of SPIE, Semiconductor Lasers and Laser
Dynamics, volume 5452, pages 51-62, 2004.
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[24]
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J. Eisner, M. Kucera and L. Recke.
Direction and stability of bifurcation branches for variational
inequalities.
J. Math. Anal. Appl., 301(2):276-294, 2005.
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[25]
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J. Eisner, M. Kucera and L. Recke.
Smooth bifurcation and variation of the contact sets for an obstacle
problem.
In Proceedings of the Equadiff 2003, Hasselt, pages 281-283.
World Scientific Publishing 2005.
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[26]
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M. Kucera, J. Eisner and L. Recke.
Smooth bifurcation and exchange of stability for variational
inequalities.
In Proceedings of the Equadiff 2003, Hasselt, pages 307-310.
World Scientific Publishing 2005.
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[27]
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D. K. Palagachev, L. Recke and L. G. Softova.
Applications of differential calculus to nonlinear elliptic boundary
value problems with discontinuous coefficients.
Preprint 2004-21, Institut für Mathematik, Humboldt-Universität
zu Berlin, 2004. Math. Annalen, 336: 617-637, 2006.
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[28]
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J. Eisner, M. Kucera and L. Recke.
Smooth dependence on parameters for solutions to variational
inequalities.
Nonlinear Anal., Theory Methods Appl., 62(2): 849-861, 2005.
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[29]
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M. Kucera, J. Eisner and L. Recke.
A global bifurcation result for variational inequalities.
In Advances in Elliptic and Parabolic Problems. A special tribute to the work of H. Amann.
Progress in Nonl. Diff. Equat. vol. 64,
ed. by M. Chipot and J. Escher, pages 253-264,
Birkhäuser, Basel,
2005.
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[30]
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N. N. Nefedov, O. E. Omel'chenko and L. Recke.
Internal layer solutions in quasilinear integro-differential equations.
Preprint 2005-16, Institut für Mathematik, Humboldt-Universität
zu Berlin, 2005. Computational Math. and Math. Physics, 46(4): 594-615, 2006.
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[31]
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A. M. Samoilenko and L. Recke.
Synchronization conditions for an oscillating system.
Ukrain. Math. J., 57(7): 922-945, 2005.
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[32]
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K. Gröger and L. Recke.
Applications of differential calculus to quasilinear elliptic
boundary value problems with non-smooth data.
Nonlinear Differ. Equations Appl. (NoDEA), 13(3): 263-285, 2006.
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[33]
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J. Eisner, M. Kucera and L. Recke.
Bifurcation direction and exchange of stability for variational inequalities on nonconvex sets.
Nonlinear Anal., Theory Methods Appl., 67:1082-1101, 2006.
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[34]
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J. Eisner, M. Kucera and L. Recke.
Smooth bifurcation for variational inequalities based on Lagrange
multipliers.
Differ. Integral Equat., 19(9): 981-1000, 2006.
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[35]
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M. Lichtner,
M. Radziunas and L. Recke.
Well-posedness, smooth dependence and center manifold reduction for a semilinear
hyperbolic system from laser dynamics.
Math. Methods Appl. Sci., 30: 931-960, 2007.
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[36]
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I. Kmit and L. Recke.
Fredholm alternative for periodic-Dirichlet problems for linear hyperbolic systems.
Preprint 342, DFG Research Center Matheon, 2006.
J. Math. Anal. Appl., 335: 355-370, 2007.
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[37]
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L. Recke, M. Wolfrum and S. Yanchuk.
Dynamics of coupled semiconductor lasers.
In Analysis and Control of Complex Nonlinear Processes in Physics, Chemestry and Biology.
World Scientific Lecture Notes in Complex Systems. vol. 5,
ed. by L. Schimansky-Geier, B. Fiedler, J. Kurths and E. Schöll, pages 185-212,
World Scientific,
2007.
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[38]
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O. E. Omel'chenko and L. Recke.
Boundary layer solutions to singularly perturbed problems via the implicit function theorem.
Preprint 2007-20, Institut für Mathematik, Humboldt-Universität
zu Berlin, 2007. Asymptotic Analysis, 62: 207-225, 2009.
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[39]
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L. Recke and O. E. Omel'chenko.
Boundary layer solutions to problems with infinite dimensional singular and regular perturbations.
Preprint 2007-21, Institut für Mathematik, Humboldt-Universität
zu Berlin, 2007. J. Differ. Equations, 245(12): 3806-3822, 2008.
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[40]
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N. N. Nefedov, A. G. Nikitin and L. Recke.
Moving fronts in integro-parabolic reaction-diffusion-advection equations.
Preprint 2007-22, Institut für Mathematik, Humboldt-Universität
zu Berlin, 2007.
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[41]
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V. F. Butuzov, N. N. Nefedov, L. Recke and K. R. Schneider.
Existence and stability of solutions with periodically moving weak internal layers.
Preprint 1294, Weierstraß-Institut für Angewandte Analysis und Stochastik Berlin, 2008.
J. Math. Anal. Appl., 348: 508-515, 2008.
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[42]
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G. Kitavtsev, L. Recke and B.Wagner.
Spectrum asymptotics for the linearized thin film equation.
Proc. Appl. Math. Mech. (PAMM), 8: 10727-10728, 2008.
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[43]
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N. N. Nefedov, L. Recke and K. R. Schneider.
Exponential asymptotic stability via Krein-Rutman theorem for singularly perturbed parabolic periodic Dirichlet problems.
Preprint 1333, Weierstraß-Institut für Angewandte Analysis und Stochastik Berlin, 2008.
Regular and Chaotic Dynamics, 15: 382-389, 2010.
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[44]
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J. A. Griepentrog and L. Recke.
Local existence, uniqueness, and smooth dependence for nonsmooth quasilinear parabolic problems.
Preprint 658, DFG Research Center MATHEON, 2009.
J. Evolution Equations, 10: 341-375, 2010.
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[45]
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J. Eisner, M. Kucera and L. Recke.
Smooth dependence on data of solutions and contact regions for a Signorini problem.
Nonlinear Anal., Theory Methods Appl. 72: 1358-1378, 2010.
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[46]
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I. Kmit and L. Recke.
Fredholmness and smooth dependence for linear hyperbolic periodic-Dirichlet problems.
Preprint 701, DFG Research Center Matheon, 2010.
J. Differ. Equations, 252: 1962-1986, 2012.
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[47]
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L. Recke, A. Samoilenko, A. Teplinsky, V. Tkachenko and S. Yanchuk.
Frequency locking of modulated waves.
Preprint 707, DFG Research Center Matheon, 2010.
Discrete and Continuous Dynamical Systems - Series A (DCDS - A),
31: 847-875, 2011.
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[48]
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J. Eisner, M. Kucera and L. Recke.
Smooth bifurcation branches of solutions for a Signorini problem.
Nonlinear Anal., Theory Methods Appl., 74: 1853-1877, 2011.
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[49]
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G. Kitavtsev, L. Recke and B.Wagner.
Asymptotics for the spectrum of a thin film equation in a singular limit.
Preprint 1555, Weierstraß-Institut für Angewandte Analysis und Stochastik Berlin, 2010.
SIAM J. Appl. Dyn. Syst., 11: 1425-1457.
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[50]
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G. Kitavtsev, L. Recke and B.Wagner.
Center manifold reduction approach for the lubrication equation.
Preprint 1554, Weierstraß-Institut für Angewandte Analysis und Stochastik Berlin, 2010.
Nonlinearity, 24: 1-23, 2011.
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[51]
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O. E. Omel'chenko and L. Recke.
Existence, local uniqueness and asymptotic approximation of spike solutions
to singularly perturbed elliptic problems.
Preprint 1607, Weierstraß-Institut für Angewandte Analysis und Stochastik Berlin, 2011.
Hiroshima Math. J., 45 (1): 35-89, 2014.
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[52]
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N. N. Nefedov, A. G. Nikitin, M. A. Petrova and L. Recke.
Moving fronts in integro-parabolic reaction-advection-diffusion equations.
Differ. Equations, 47 (9): 1305-1319, 2011.
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[53]
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V. F. Butuzov, N. N. Nefedov, L. Recke and K. R. Schneider.
Region of attraction of a periodic solution to a singularly perturbed parabolic problem.
Applicable Anal., 91 (7): 1265-1277, 2012.
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[54]
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L. Recke, A. Samoilenko, A. Tkachenko and S. Yanchuk.
Frequency locking by external forcing in systems with rotational symmetry.
SIAM J. Appl. Dyn. Syst., 11: 771-800, 2012.
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[55]
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J. Eisner, M. Kucera and L. Recke.
Smooth bifurcation for a Signorini problem on a rectangle.
Mathematica Bohemica, 137: 131-138, 2012.
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[56]
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V. F. Butuzov, N. N. Nefedov, L. Recke and K. R. Schneider.
On a singularly perturbed initial value problem in the case of a double root of the degenerate equation.
Nonl. Anal., Theory Methods Appl., 83: 1-11, 2013.
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[57]
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I. Kmit and L. Recke.
Periodic solutions to dissipative hyperbolic systems. I: Fredholm solvability of linear problems.
Preprint 999, DFG Research Center Matheon, 2013.
Differ. Integral Equat., 29: 1049-1070, 2016.
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[58]
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I. Kmit and L. Recke.
Periodic solutions to dissipative hyperbolic systems. II: Hopf bifurcation for semilinear problems.
Preprint 1000, DFG Research Center Matheon, 2013. J. Differ. Equations, 257:264-309, 2014.
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[59]
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I. Kmit, L. Recke and V. Tkachenko.
Robustness of exponential dichotomies of boundaty-value problems for general first-order hyperbolic systems.
Preprint 998, DFG Research Center Matheon, 2013. Ukrain. Math. J., 65(2): 260-276, 2013.
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[60]
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N. N. Nefedov, L. Recke and K. R. Schneider.
Existence and asymptotic stability of periodic solutions with
an interior layer of reaction-advection-diffusion equations.
J. Math. Anal. Appl., 405: 90-103, 2013.
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[61]
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N. N. Nefedov, L. Recke and K. R. Schneider.
Periodic solutions with a boundary layer of reaction-diffusion equations with singularly perturbed Neumann boundary conditions.
J. Bifurcation Chaos Appl. Sci. Eng., 24 (8): ID 1440019, 2014.
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[62]
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I. Kmit and L. Recke.
Time-periodic second-order hyperbolic equations: Fredholmness, regularity and smooth dependence. In:
Operator Theory: Advances and Applications, Vol. 245, 147-181, Springer, 2015.
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[63]
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I. Kmit and L. Recke.
Solution regularity and smooth dependence for abstract equations and applications to hyperbolic PDEs. J. Differential Equations.
259: 6287-6337, 2015.
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[64]
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J. Eisner, M. Kucera and L. Recke.
Direction and stability of bifurcating solutions for a Signorini problem.
Nonlinear Anal., Theory Methods Appl., Ser. A 113: 357-371, 2015.
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[65]
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V. F. Butuzov, N. N. Nefedov, O.E. Omel'chenko, L. Recke and K. R. Schneider.
Time-periodic boundary layer solutions to singularly perturbed parabolic problems.
WIAS Preprint., 2300, 2016, J. Differential Equations 262: 4823--4862, 2017.
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[66]
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R. Klyuchnyk, I. Kmit, and L. Recke.
Exponential dichotomy for hyperbolic systems with periodic boundary conditions.
J. Differential Equations 262:2493-2520, 2016.
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[67]
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V.F. Butuzov, N.N. Nefedov, O.E. Omel'chenko, L. Recke and K.R. Schneider.
An implicit function theorem and applications to nonsmooth boundary layers.
In: Patterns of Dynamics.
Proc. Int. Conf. in honor of B. Fiedler, ed. by
P. Gurevich, J. Hell, B. Sandstede, A. Scheel, Springer Proc. in Mathematics & Statistics vol. 205: 111--127, 2017.
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[68]
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L. Recke, M. Väth, M. Kucera and J. Navratil.
Crandall-Rabiniwitz type bifurcation for non-differentiable perturbations of smooth mappings.
In: Patterns of Dynamics.
Proc. Int. Conf. in honor of B. Fiedler, ed. by
P. Gurevich, J. Hell, B. Sandstede, A. Scheel, Springer Proc. in Mathematics & Statistics vol. 205: 184--202, 2017.
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[69]
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D.V. Lukyanenko, V.T. Volkov, N.N. Nefedov, L. Recke and K.R. Schneider.
Analytical-numerical approach to solving
singularly perturbed parabolic equations with the use of dynamic adapted meshes.
Model. Anal. Inf. Sist. 23: 334--341, 2016.
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[70]
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V.F. Butuzov, N.N. Nefedov, L. Recke and K.R. Schneider.
Asymptotics, stability and region of attraction of a periodic
solution to a singularly perturbed parabolic problem with double root of the degenerate equation.
Autom. Control Comput. Sciences 51: 248--258, 2016.
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[71]
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O.E. Omel'chenko, L. Recke, V.F. Butuzov and N.N. Nefedov.
Time-periodic boundary layer solutions to singularly perturbed parabolic problems.
J. Differ. Equations 262:4823-4862,2017.
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[72]
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V.F. Butuzov, N.N. Nefedov, L. Recke and K.R. Schneider.
Existence, asymptotics, stability and region of attraction of a periodic boundary layer
solution in case of a double root of the degenerate equation.
Comp. Math. Math. Phys. 58: 1989--2001, 2018.
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[73]
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L. Recke.
Forced frequency locking for differential equations with distributional forcings.
Dedicated to A.M. Samoilenko on the occasion of his eighttieth birthday.
Ukrainian Math. J., 70:115-129, 2018.
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[74]
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N.N. Nefedov, E.I. Nikulin and L. Recke.
On the existence and asymptotic stability of periodic contrast structures in quasilinear reaction-advection-diffusion equations.
Russ. J. Math. Phys., 26:55-69, 2019.
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[75]
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V.F. Butuzov, N.N. Nefedov, O.E. Omel'chenko and L. Recke.
Partly dissipative systems with multizonal initial and boundary layers.
Jounal of Physics: Conf. Series., 1205, 2019.
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[76]
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I. Kmit, L. Recke and V. Tkachenko.
Classical bounded and almost periodic solutions to quasilinear first-order systems in a strip.
J. Differ. Equations 2020.
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