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