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2013
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Nikolai Nefedov

Lomonosov Moscow State University,GSP-1, Leninskie Gory, Moscow, 119992, Russia
Faculty of Physics, M.V. Lomonosov Moscow State University

Publications:

Nefedov N. N., Recke L., Schneider K. R.
Asymptotic stability via the Krein–Rutman theorem for singularly perturbed parabolic periodic Dirichlet problems
2010, vol. 15, no. 2-3, pp.  382-389
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
Citation: Nefedov N. N., Recke L., Schneider K. R.,  Asymptotic stability via the Krein–Rutman theorem for singularly perturbed parabolic periodic Dirichlet problems, Regular and Chaotic Dynamics, 2010, vol. 15, no. 2-3, pp. 382-389
DOI:10.1134/S1560354710020231

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