On a uniform estimate for positive solutions of semilinear elliptic equations

Sourdis, Christos (2012) On a uniform estimate for positive solutions of semilinear elliptic equations. (Unpublished)

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Abstract

We consider semilinear elliptic equations with Dirichlet boundary conditions in a Lipschitz, possibly unbounded, domain. Under suitable assumptions on the nonlinearity, we deduce a condition on the size of the domain that implies the existence of a positive solution satisfying a uniform pointwise estimate. Here, uniform means that the estimate is independent of the domain. Besides of its simplicity, the main advantage of our approach is that we can remove a restrictive assumption on the nonlinearity that was imposed in a recent paper. Moreover, we can remove a non-degeneracy condition that was assumed in the latter paper.

Item Type: Article
Subjects: Q Science > QA Mathematics
Depositing User: Dr. Christos Sourdis
Date Deposited: 16 Jul 2012 10:09
Last Modified: 12 May 2017 07:17
URI: http://preprints.acmac.uoc.gr/id/eprint/137

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