Solutions of an anisotropic nonlocal problem involving variable exponent

Mustafa Avci, Rabil A. Ayazoglu, Bilal Cekic

Research output: Contribution to journalJournal Articlepeer-review

7 Citations (Scopus)


The present paper deals with an anisotropic Kirchhoff problem under homogeneous Dirichlet boundary conditions, set in a bounded smooth domain Ω of ℝN (N ≥ 3). The problem studied is a stationary version of the original Kirchhoff equation, involving the anisotropic p(.)-Laplacian operator, in the framework of the variable exponent Lebesgue and Sobolev spaces. The question of the existence of weak solutions is treated. Applying the Mountain Pass Theorem of Ambrosetti and Rabinowitz, the existence of a nontrivial weak solution is obtained in the anisotropic variable exponent Sobolev space W01p→(.) (Ω), provided that the positive parameter λ that multiplies the nonlinearity f is small enough.

Original languageEnglish
Pages (from-to)325-338
Number of pages14
JournalAdvances in Nonlinear Analysis
Issue number3
Publication statusPublished - 1 Aug. 2013


  • Anisotropic p (·)-Laplacian
  • Anisotropic variable exponent Lebesgue-Sobolev spaces
  • Mountain Pass Theorem
  • Nonlocal problem


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