JournalsrsmupVol. 136pp. 95–109

Existence and multiplicity of solutions for a p(x)p(x)-Kirchhoff type equation

  • Ghasem A. Afrouzi

    University of Mazandaran, Babolsar, Iran
  • Maryam Mirzapour

    University of Mazandaran, Babolsar, Iran
  • Nguyen Thanh Chung

    Quang Binh University, Vietnam
Existence and multiplicity of solutions for a $p(x)$-Kirchhoff type equation cover
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Abstract

This paper is concerned with the existence and multiplicity to p(x)p(x)-Kirchhoff type problem of the following form

-M \big{(} \int_{\Omega}\frac{1}{p(x)}|\nabla u|^{p(x)}dx\big {)}\mathrm{div}(|\nabla u|^{p(x)-2}\nabla u) =f(x,u) \quad \text{in } \Omega,
u=0onΩ.u=0 \quad \mathrm {on} \: \partial \Omega.

By means of a direct variational approach and the theory of the variable exponent Sobolev spaces, we establish conditions ensuring the existence and multiplicity of solutions for the problem.

Cite this article

Ghasem A. Afrouzi, Maryam Mirzapour, Nguyen Thanh Chung, Existence and multiplicity of solutions for a p(x)p(x)-Kirchhoff type equation. Rend. Sem. Mat. Univ. Padova 136 (2016), pp. 95–109

DOI 10.4171/RSMUP/136-8