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

Khaled Kefi; Kamel Saoudi; Mohammed Mosa AL-Shomrani

doi:10.4171/zaa/1678

JournalszaaVol. 40, No. 2pp. 167–182

A Kirchhoff $p (x)$ -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

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Abstract

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

(P_{\pm λ}) {M (t) Δ (∣Δ u ∣^{p (x) - 2} Δ u) Δ u = a (x) u^{- γ (x)} \pm λ u^{q (x) - 2} u, = u = 0, in Ω, on \partial Ω,

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 $p (x)$ -Biharmonic Problem Involving Singular Nonlinearities and Navier Boundary Conditions. Z. Anal. Anwend. 40 (2021), no. 2, pp. 167–182

DOI 10.4171/ZAA/1678