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1997 Existence of extremal periodic solutions for quasilinear parabolic equations
Siegfried Carl
Abstr. Appl. Anal. 2(3-4): 257-270 (1997). DOI: 10.1155/S1085337597000389


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.


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Siegfried Carl. "Existence of extremal periodic solutions for quasilinear parabolic equations." Abstr. Appl. Anal. 2 (3-4) 257 - 270, 1997.


Published: 1997
First available in Project Euclid: 14 April 2003

zbMATH: 0942.35014
MathSciNet: MR1704872
Digital Object Identifier: 10.1155/S1085337597000389

Primary: 35B05 , 35B10
Secondary: 35K60 , 47N20

Keywords: Dirichlet-periodic boundary conditions , extremal solutions , pseudomonotone operators , quasilinear parabolic equations , truncation and comparison techniques , upper and lower solutions

Rights: Copyright © 1997 Hindawi

Vol.2 • No. 3-4 • 1997
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