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The eigenvalue problem for the p -Laplacian-like equations

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  • Zu-Chi Chen
  • Tao Luo

Abstract

We consider the eigenvalue problem for the following p -Laplacian-like equation: − div ( a ( | D u | p ) | D u | p − 2 D u ) = λ f ( x , u ) in Ω , u = 0 on ∂ Ω , where Ω ⊂ ℝ n is a bounded smooth domain. When λ is small enough, a multiplicity result for eigenfunctions are obtained. Two examples from nonlinear quantized mechanics and capillary phenomena, respectively, are given for applications of the theorems.

Suggested Citation

  • Zu-Chi Chen & Tao Luo, 2003. "The eigenvalue problem for the p -Laplacian-like equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-12, January.
    • Handle: RePEc:hin:jijmms:507280
    DOI: 10.1155/S0161171203006744
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