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, Volume 15, Numbers 2-3,
pp. 382-389