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.
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
\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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https://www.mathnet.ru/eng/rcd503
https://www.mathnet.ru/eng/rcd/v15/i2/p382
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