A variational approach to superlinear semipositone elliptic problems

Document Type

Article

Publication Date

1-1-2017

Publication Title

Proceedings of the American Mathematical Society

Volume

145

Issue

6

First page number:

2661

Last page number:

2675

Abstract

In this paper we present a variational approach to a class of elliptic problems with superlinear semipositone nonlinearities. We consider the parametrized family of problems (Formula presented) with l > 0, a continuous, and f subcritical and superlinear at infinity. We obtain positive solutions of such problems for 0 < λ < λ0 by combining a suitable rescaling with a continuity argument. In doing so, we require f to be of regular variation at infinity, so that f does not need to be asymptotic to a power. Furthermore, a may vanish in open parts of Ω or change sign. © 2016 American Mathematical Society.

Language

english

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