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Regular and Chaotic Dynamics, 2010, Volume 15, Issue 2-3, Pages 382–389
DOI: https://doi.org/10.1134/S1560354710020231 (Mi rcd503) 		 
This article is cited in 7 scientific papers (total in 7 papers)

On the 75th birthday of Professor L.P. Shilnikov

Asymptotic stability via the Krein–Rutman theorem for singularly perturbed parabolic periodic Dirichlet problems

N. N. Nefedova, L. Reckeb, K. R. Schneiderc

a Faculty of Physics, M.V. Lomonosov Moscow State University, Leninskie Gory, Moscow, 119991 Russia
b Humboldt-Universität zu Berlin, Institut für Mathematik, Unter den Linden 6, D-10099 Berlin, Germany
c Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany
Citations (7)
DOI: https://doi.org/10.1134/S1560354710020231
Abstract: We consider singularly perturbed semilinear parabolic periodic problems and assume the existence of a family of solutions. We present an approach to establish the exponential asymptotic stability of these solutions by means of a special class of lower and upper solutions. The proof is based on a corollary of the Krein–Rutman theorem.
Keywords: singularly perturbed parabolic Dirichlet problems, exponential asymptotic stability, Krein–Rutman theorem, lower and upper solutions.
Received: 05.11.2009
Accepted: 12.12.2009
Bibliographic databases:
Document Type: Personalia
MSC: 35B10, 35B25, 35B35, 35K58, 35K90
Language: English
Citation: N. N. Nefedov, L. Recke, K. R. Schneider, “Asymptotic stability via the Krein–Rutman theorem for singularly perturbed parabolic periodic Dirichlet problems”, Regul. Chaotic Dyn., 15:2-3 (2010), 382–389
Citation in format AMSBIB
\Bibitem{NefRecSch10}
\by N. N. Nefedov, L. Recke, K. R. Schneider
\paper Asymptotic stability via the Krein–Rutman theorem for singularly perturbed parabolic periodic Dirichlet problems
\jour Regul. Chaotic Dyn.
\yr 2010
\vol 15
\issue 2-3
\pages 382--389
\mathnet{http://mi.mathnet.ru/rcd503}
\crossref{https://doi.org/10.1134/S1560354710020231}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2644345}
\zmath{https://zbmath.org/?q=an:1211.35023}
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