Existence of extremal periodic solutions for quasilinear parabolic equations

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 u...

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Main Author:	Siegfried Carl
Format:	Article
Language:	English
Published:	Hindawi Limited 1997-01-01
Series:	Abstract and Applied Analysis
Subjects:	Quasilinear parabolic equations Dirichlet-periodic boundary conditions extremal solutions upper and lower solutions pseudomonotone operators truncation and comparison techniques.
Online Access:	http://dx.doi.org/10.1155/S1085337597000389

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spelling	doaj-01de9b620bec46969e6f5d253414a4562020-11-25T02:02:31ZengHindawi LimitedAbstract and Applied Analysis1085-33751997-01-0123-425727010.1155/S1085337597000389Existence of extremal periodic solutions for quasilinear parabolic equationsSiegfried Carl0Martin-Luther-Universität Halle-Wittenberg, Fachbereich Mathematik und Informatik, Institut für Analysis, Halle D-06099, GermanyIn 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.http://dx.doi.org/10.1155/S1085337597000389Quasilinear parabolic equationsDirichlet-periodic boundary conditionsextremal solutionsupper and lower solutionspseudomonotone operatorstruncation and comparison techniques.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Siegfried Carl
spellingShingle	Siegfried Carl Existence of extremal periodic solutions for quasilinear parabolic equations Abstract and Applied Analysis Quasilinear parabolic equations Dirichlet-periodic boundary conditions extremal solutions upper and lower solutions pseudomonotone operators truncation and comparison techniques.
author_facet	Siegfried Carl
author_sort	Siegfried Carl
title	Existence of extremal periodic solutions for quasilinear parabolic equations
title_short	Existence of extremal periodic solutions for quasilinear parabolic equations
title_full	Existence of extremal periodic solutions for quasilinear parabolic equations
title_fullStr	Existence of extremal periodic solutions for quasilinear parabolic equations
title_full_unstemmed	Existence of extremal periodic solutions for quasilinear parabolic equations
title_sort	existence of extremal periodic solutions for quasilinear parabolic equations
publisher	Hindawi Limited
series	Abstract and Applied Analysis
issn	1085-3375
publishDate	1997-01-01
description	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.
topic	Quasilinear parabolic equations Dirichlet-periodic boundary conditions extremal solutions upper and lower solutions pseudomonotone operators truncation and comparison techniques.
url	http://dx.doi.org/10.1155/S1085337597000389
work_keys_str_mv	AT siegfriedcarl existenceofextremalperiodicsolutionsforquasilinearparabolicequations
_version_	1724952376449695744

Existence of extremal periodic solutions for quasilinear parabolic equations

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