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25 June 2002 Perturbations near resonance for the $p$-Laplacian in $\mathbb{R}^N$
To Fu Ma, Maurício Luciano Pelicer
Abstr. Appl. Anal. 7(6): 323-334 (25 June 2002). DOI: 10.1155/S1085337502203073


We study a multiplicity result for the perturbed p-Laplacian equation Δpuλg(x)|u|p2u=f(x,u)+h(x)inN, where 1<p<N and λ is near λ1, the principal eigenvalue of the weighted eigenvalue problem Δpu=λg(x)|u|p2u in N. Depending on which side λ is from λ1, we prove the existence of one or three solutions. This kind of result was firstly obtained by Mawhin and Schmitt (1990) for a semilinear two-point boundary value problem.


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To Fu Ma. Maurício Luciano Pelicer. "Perturbations near resonance for the $p$-Laplacian in $\mathbb{R}^N$." Abstr. Appl. Anal. 7 (6) 323 - 334, 25 June 2002.


Published: 25 June 2002
First available in Project Euclid: 14 April 2003

zbMATH: 1065.35116
MathSciNet: MR1920146
Digital Object Identifier: 10.1155/S1085337502203073

Primary: 35A15 , 35J60

Rights: Copyright © 2002 Hindawi

Vol.7 • No. 6 • 25 June 2002
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