Abstract and Applied Analysis
Volume 2 (1997), Issue 3-4, Pages 257-270

Existence of extremal periodic solutions for quasilinear parabolic equations

Siegfried Carl

Martin-Luther-Universität Halle-Wittenberg, Fachbereich Mathematik und Informatik, Institut für Analysis, Halle D-06099, Germany

Received 18 August 1997

Copyright © 1997 Siegfried Carl. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper we consider a quasilinear parabolic equation in a bounded domain under periodic Dirichlet boundary conditions. Our main goal is to prove the existence of extremal solutions among all solutions lying in a sector formed by appropriately defined upper and lower solutions. The main tools used in the proof of our result are recently obtained abstract results on nonlinear evolution equations, comparison and truncation techniques and suitably constructed special testfunction.