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Combined concave–convex effects in anisotropic elliptic equations with variable exponent

  • Vicenţiu D. Rădulescu
  • Ionela-Loredana Stăncuţ
Article

Abstract

We establish the existence and multiplicity of solutions for a class of quasilinear elliptic equations involving the anisotropic \({\vec{p}(\cdot)}\)-Laplace operator, on a bounded domain with smooth boundary. We work on the weighted anisotropic variable exponent Sobolev space and our main tools are Sobolev embeddings and the mountain pass theorem.

Keywords

Quasilinear elliptic equations \({\vec{p}(\cdot)}\)-Laplace operator Weighted anisotropic variable exponent Sobolev space Critical point Weak solution 

Mathematics Subject Classification

35J60 58E05 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  • Vicenţiu D. Rădulescu
    • 1
    • 2
  • Ionela-Loredana Stăncuţ
    • 2
  1. 1.Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia
  2. 2.Simion Stoilow Mathematics Institute of the Romanian AcademyBucharestRomania

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