A degenerate Kirchhoff-type problem involving variable s(⋅)-order fractional p(⋅)-Laplacian with weights

2023/08/15 by Mostafa Allaoui, Allaoui, Mostafa, Mohamed Karim Hamdani +3
Mathematics · #Spectral Theory in Mathematical Physics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2308.08007

Abstract

This paper deals with a class of nonlocal variable s(.)-order fractional p(.)-Kirchhoff type equations: \ K(∫_ℝ^2N(1)/(p(x,y))\frac|φ(x)-φ(y)|^p(x,y)|x-y|^N+s(x,y)p(x,y) dx dy)(-Δ)^s(⋅)_p(⋅)φ(x) =f(x,φ) in Ω,
φ=0 on ℝ^N\backslashΩ. . Under some suitable conditions on the functions p,s, K and f, the existence and multiplicity of nontrivial solutions for the above problem are obtained. Our results cover the degenerate case in the p(⋅) fractional setting.

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