Abstract and Applied Analysis

Positive solutions of higher order quasilinear elliptic equations

Marcelo Montenegro

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Abstract

The higher order quasilinear elliptic equation Δ(Δp(Δu))=f(x,u) subject to Dirichlet boundary conditions may have unique and regular positive solution. If the domain is a ball, we obtain a priori estimate to the radial solutions via blowup. Extensions to systems and general domains are also presented. The basic ingredients are the maximum principle, Moser iterative scheme, an eigenvalue problem, a priori estimates by rescalings, sub/supersolutions, and Krasnosel′skiĭ fixed point theorem.

Article information

Source
Abstr. Appl. Anal., Volume 7, Number 8 (2002), 423-452.

Dates
First available in Project Euclid: 14 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1050348373

Digital Object Identifier
doi:10.1155/S1085337502204030

Mathematical Reviews number (MathSciNet)
MR1930826

Zentralblatt MATH identifier
1044.35021

Subjects
Primary: 35J55 35A05
Secondary: 35J60: Nonlinear elliptic equations

Citation

Montenegro, Marcelo. Positive solutions of higher order quasilinear elliptic equations. Abstr. Appl. Anal. 7 (2002), no. 8, 423--452. doi:10.1155/S1085337502204030. https://projecteuclid.org/euclid.aaa/1050348373


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