JournalszaaVol. 40, No. 2pp. 167–182

A Kirchhoff p(x)p(x)-Biharmonic Problem Involving Singular Nonlinearities and Navier Boundary Conditions

  • Khaled Kefi

    Université de Tunis El Manar, Tunisia

  • Kamel Saoudi

    Imam Abdulrahman Bin Faisal University, Dammam, Saudi Arabia

  • Mohammed Mosa AL-Shomrani

    King Abdulaziz University, Jeddah, Saudi Arabia
A Kirchhoff $p(x)$-Biharmonic Problem Involving Singular Nonlinearities and Navier Boundary Conditions cover
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Abstract

The aim of this work is to study the existence of weak solutions for a nonhomogeneous singular p(x)p(x)-Kirchhoff problem of the following form

(P±λ){M(t)Δ(∣Δu∣p(x)−2Δu)=a(x)u−γ(x)±λuq(x)−2u, inΩ,Δu=u=0, on∂Ω,(\textbf{P}_{\pm \lambda}) \quad \left\{ \begin{aligned} M(t)\Delta(|\Delta u|^{p(x)-2}\Delta u) &=a(x) u^{-\gamma (x)}\pm \lambda u^{q(x)-2}u, &\ &\quad \mathrm{in} \quad \Omega, \\ \Delta u&=u=0, &\ &\quad \mathrm{on} \quad\partial\Omega, \end{aligned} \right.

by using variational techniques and monotonicity arguments combined with the theory of the generalized Lebesgue Sobolev spaces.

Cite this article

Khaled Kefi, Kamel Saoudi, Mohammed Mosa AL-Shomrani, A Kirchhoff p(x)p(x)-Biharmonic Problem Involving Singular Nonlinearities and Navier Boundary Conditions. Z. Anal. Anwend. 40 (2021), no. 2, pp. 167–182

DOI 10.4171/ZAA/1678