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Perturbations near resonance for the p -Laplacian in â„ N

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  • To Fu Ma
  • Maurício Luciano Pelicer

Abstract

We study a multiplicity result for the perturbed p -Laplacian equation − Δ p u − λ g ( x ) | u | p − 2 u = f ( x , u ) + h ( x )   in   ℠N , where 1 < p < N and λ is near λ   1 , the principal eigenvalue of the weighted eigenvalue problem − Δ p u = λ g ( x ) | u | p − 2 u in ℠N . Depending on which side λ is from λ   1 , 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.

Suggested Citation

  • To Fu Ma & Maurício Luciano Pelicer, 2002. "Perturbations near resonance for the p -Laplacian in â„ N," Abstract and Applied Analysis, Hindawi, vol. 7, pages 1-12, January.
    • Handle: RePEc:hin:jnlaaa:473628
    DOI: 10.1155/S1085337502203073
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