WIAS Preprint No. 1333, (2008)

Exponential asymptotic stability via Krein--Rutman theorem for singularly perturbed parabolic periodic Dirichlet problems


  • Nefedov, Nikolai N.
  • Recke, Lutz
  • Schneider, Klaus R.

2010 Mathematics Subject Classification

  • 35B25 35B10 35B35 35K10 35K90


  • 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.

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