Abstract and Applied Analysis

Abstract and Applied Analysis / 1997 / Article

Open Access

Volume 2 |Article ID 743028 | https://doi.org/10.1155/S1085337597000389

Siegfried Carl, "Existence of extremal periodic solutions for quasilinear parabolic equations", Abstract and Applied Analysis, vol. 2, Article ID 743028, 14 pages, 1997. https://doi.org/10.1155/S1085337597000389

Existence of extremal periodic solutions for quasilinear parabolic equations

Received18 Aug 1997

Abstract

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.

Copyright © 1997 Hindawi Publishing Corporation. 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.


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