Abstract and Applied Analysis

Existence of extremal periodic solutions for quasilinear parabolic equations

Siegfried Carl

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2, Number 3-4 (1997), 257-270.

Dates
First available in Project Euclid: 14 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1050355237

Digital Object Identifier
doi:10.1155/S1085337597000389

Mathematical Reviews number (MathSciNet)
MR1704872

Zentralblatt MATH identifier
0942.35014

Subjects
Primary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 35B10
Secondary: 35K60 47N20

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

Citation

Carl, Siegfried. Existence of extremal periodic solutions for quasilinear parabolic equations. Abstr. Appl. Anal. 2 (1997), no. 3-4, 257--270. doi:10.1155/S1085337597000389. https://projecteuclid.org/euclid.aaa/1050355237


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