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2012 Nonhomogeneous Nonlinear Dirichlet Problems with a p -Superlinear Reaction
Leszek Gasiński, Nikolaos S. Papageorgiou
Abstr. Appl. Anal. 2012(SI17): 1-28 (2012). DOI: 10.1155/2012/918271


We consider a nonlinear Dirichlet elliptic equation driven by a nonhomogeneous differential operator and with a Carathéodory reaction f ( z , ζ ) , whose primitive f ( z , ζ ) is p -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 p -Laplacian, the ( p , q ) -Laplacian, and the p -generalized mean curvature operator.


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Leszek Gasiński. Nikolaos S. Papageorgiou. "Nonhomogeneous Nonlinear Dirichlet Problems with a p -Superlinear Reaction." Abstr. Appl. Anal. 2012 (SI17) 1 - 28, 2012.


Published: 2012
First available in Project Euclid: 5 April 2013

zbMATH: 1246.35087
MathSciNet: MR2922949
Digital Object Identifier: 10.1155/2012/918271

Rights: Copyright © 2012 Hindawi

Vol.2012 • No. SI17 • 2012
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