Nonhomogeneous Nonlinear Dirichlet Problems with a -Superlinear Reaction

Leszek Gasiński and Nikolaos S. Papageorgiou

Abstract and Applied Analysis, 2012, vol. 2012, 1-28

Abstract:

We consider a nonlinear Dirichlet elliptic equation driven by a nonhomogeneous differential operator and with a Carathéodory reaction , whose primitive is -superlinear near , but need not satisfy the usual in such cases, the Ambrosetti-Rabinowitz condition. Using a combination of variational methods with the Morse theory (critical groups), we show that the problem has at least three nontrivial smooth solutions. Our result unifies the study of “superlinear†equations monitored by some differential operators of interest like the -Laplacian, the -Laplacian, and the -generalized mean curvature operator.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:918271

DOI: 10.1155/2012/918271

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