On Existence of Solution for a Class of Semilinear Elliptic Equations with Nonlinearities That Lies between Different Powers

Claudianor O. Alves and Marco A. S. Souto

Abstract and Applied Analysis, 2008, vol. 2008, 1-6

Abstract:

We prove that the semilinear elliptic equation , in , , on has a positive solution when the nonlinearity belongs to a class which satisfies at infinity and behaves like near the origin, where if and if . In our approach, we do not need the Ambrosetti-Rabinowitz condition, and the nonlinearity does not satisfy any hypotheses such those required by the blowup method. Furthermore, we do not impose any restriction on the growth of .

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:578417

DOI: 10.1155/2008/578417

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