Asymptotic stability via the Krein-Rutman theorem for singularly perturbed parabolic periodic dirichlet problems

作者：Nefedov N N^*; Recke L; Schneider K R

来源：Regular & Chaotic Dynamics, 2010, 15(2-3): 382-389.

DOI：10.1134/S1560354710020231

• singularly perturbed parabolic Dirichlet problems
• exponential asymptotic stability
• Krein-Rutman theorem
• lower and upper solutions

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.

• 出版日期2010-6