Resonance and nonresonance for p-Laplacian problems with weighted eigenvalues conditions

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December 2009, 25(4): 1219-1227. doi: 10.3934/dcds.2009.25.1219

Resonance and nonresonance for p-Laplacian problems with weighted eigenvalues conditions

Francisco Odair de Paiva ^1, and Humberto Ramos Quoirin ^2,

1.	Departamento de Matemática, IMECC - UNICAMP , Caixa Postal 6065, 13081-970 Campinas-SP, Brazil
2.	ULB, CP 214 Bd du Triomphe, B-1050 Bruxelles, Belgium

Received December 2007 Revised July 2009 Published September 2009

Abstract
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We study multiplicity of solutions for a quasilinear elliptic problem related to the $p$-Laplacian operator. Our assumptions rely on the first eigenvalue depending on a weight function. We treat both resonant and non-resonant cases.

Keywords: p-Laplacian, multiplicity of solution., indefinite weight.

Mathematics Subject Classification: Primary: 35J25; Secondary: 58E0.

Citation: Francisco Odair de Paiva, Humberto Ramos Quoirin. Resonance and nonresonance for p-Laplacian problems with weighted eigenvalues conditions. Discrete & Continuous Dynamical Systems - A, 2009, 25 (4) : 1219-1227. doi: 10.3934/dcds.2009.25.1219

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