Abstract

We are concerned with questions of existence and multiplicity of positive solutions of the elliptic problem {−div  (K(∣∇u∣p)∣∇u∣p−2∇u)=λf(u)inΩ,u=0on∂Ω(Pλ)\left\{\begin{array}{rclcc} -\mathrm{div} \;(\mathcal{K}(|\nabla u|^{p})|\nabla u|^{p-2}\nabla u) & = & \lambda f(u) & \text{in} & \Omega, \\ u & = & 0 & \text{on}& \partial\Omega \end{array} \right. \tag{$P_{\lambda}$} with 1<p<∞1<p<\infty, where Ω⊂RN\Omega \subset \mathbb{R}^{N} is a bounded smooth domain, λ\lambda is a positive real parameter, K:R+→R+\mathcal{K}:\mathbb{R}^{+}\rightarrow \mathbb{R}^{+} is a C1C^{1}-function and f:R→Rf:\mathbb{R}\rightarrow \mathbb{R} is a continuous functions which changes sign. We use variational methods.

Author information

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Francisco Julio S. A. Corrêa

Dep de Matemática e Estatística, Universidade Federal de Campina Grande, 58.429-970 Campina Grande-Paraíba, Brazil

fjulio@ufpa.br

Amanda Suellen S. Corrêa

Faculdade de Matemática, Universidade Federal do Pará, 66.075-110-Belém-Pará, Brazil

João R. Santos Junior

Faculdade de Matemática, Universidade Federal do Pará, 66.075-110-Belém-Pará, Brazil

Keywords

  • Laplacian
  • variational methods
  • multiplicity of positive solutions

Mathematics Subject Classification

35J65, 34B15

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Suggested citation

F. J. S. A. Corrêa, A. S. S. Corrêa, J. R. Santos Junior. “Multiple Ordered Positive Solutions of an Elliptic Problem Involving the p&q-Laplacian.” Journal of Convex Analysis 21 (2014), No. 4, 1023–1042. https://doi.org/10.68381/jca21055

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