JournalszaaVol. 33, No. 3pp. 289–303

Existence and Multiplicity of Solutions for Kirchhoff Type Problems Involving p(x)p(x)-Biharmonic Operators

  • 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 Kirchhoff Type Problems Involving $p(x)$-Biharmonic Operators cover
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Abstract

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

{M(Ω1p(x)Δup(x)dx)Δ(Δup(x)2Δu)=f(x,u) in Ωu=Δu=0 on Ω,\left\{ \begin{alignedat}{2} M\left(\int_{\Omega}\frac{1}{p(x)}|\Delta u|^{p(x)}\,dx\right)\Delta(|\Delta u|^{p(x)-2}\Delta u) &=f(x,u)& &\text{ in } \Omega \\ u&=\Delta u =0 &\quad &\textrm{ on } \partial\Omega, \end{alignedat}\right.

by using the mountain pass theorem of Ambrosetti and Rabinowitz and Ekeland's variational principle in two cases when the Carath\'{e}odory function f(x,u)f(x,u) having special structure.

Cite this article

Ghasem A. Afrouzi, Maryam Mirzapour, Nguyen Thanh Chung, Existence and Multiplicity of Solutions for Kirchhoff Type Problems Involving p(x)p(x)-Biharmonic Operators. Z. Anal. Anwend. 33 (2014), no. 3, pp. 289–303

DOI 10.4171/ZAA/1512