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2008 On Existence of Solution for a Class of Semilinear Elliptic Equations with Nonlinearities That Lies between Different Powers
Claudianor O. Alves, Marco A. S. Souto
Abstr. Appl. Anal. 2008: 1-6 (2008). DOI: 10.1155/2008/578417

Abstract

We prove that the semilinear elliptic equation Δ u = f ( u ) , in Ω , u = 0 , on Ω has a positive solution when the nonlinearity f belongs to a class which satisfies μ t q f ( t ) C t p at infinity and behaves like t q near the origin, where 1 < q < ( N + 2 ) / ( N 2 ) if N 3 and 1 < q < + if N = 1 , 2 . 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 p .

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Claudianor O. Alves. Marco A. S. Souto. "On Existence of Solution for a Class of Semilinear Elliptic Equations with Nonlinearities That Lies between Different Powers." Abstr. Appl. Anal. 2008 1 - 6, 2008. https://doi.org/10.1155/2008/578417

Information

Published: 2008
First available in Project Euclid: 9 September 2008

zbMATH: 1187.35064
MathSciNet: MR2411040
Digital Object Identifier: 10.1155/2008/578417

Rights: Copyright © 2008 Hindawi

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