Abstract and Applied Analysis

Positive solutions of higher order quasilinear elliptic equations

Marcelo Montenegro

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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

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

First available in Project Euclid: 14 April 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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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