Positive solutions of higher order quasilinear elliptic equations

Marcelo Montenegro

Abstract and Applied Analysis, 2002, vol. 7, 1-30

Abstract:

The higher order quasilinear elliptic equation − Δ ( Δ p ( Δ u ) ) = 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.

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:613506

DOI: 10.1155/S1085337502204030

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