Multiplicity and concentration of solutions for a fractional p-Kirchhoff type equation

2021/12/29 by Wenjing Chen, Chen, Wenjing, Huayu Pan +1
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.2112.14627

arxiv created 2021/12/29 · openalex publication_date 2021/12/29 · arxiv updated 2021/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with the following fractional p-Kirchhoff equation ε ^spM( ε ^{sp - N}\iint_ℝ^2N\frac| u(x) - u(y) |^p| x - y |^{N + sp}dxdy)(-Δ)_p^su + V(x)u^{p - 1} = u^{p_s^* - 1}+f(u), u>0, in ℝ^N, %u ∈ W^s,p(ℝ^N), where ε>0 is a parameter, M(t)=a+bt^θ-1 with a>0, b>0, θ>1, (-Δ)_p^s denotes the fractional p-Laplacian operator with 0<s<1 and 1<p<∞, N>sp, θp<p_s^* with p_s^*=(Np)/(N-sp) is the fractional critical Sobolev exponent, f is a superlinear continuous function with subcritical growth and V is a positive continuous potential. Using penalization method and Ljusternik-Schnirelmann theory, we study the existence, multiplicity and concentration of nontrivial solutions for ε>0 small enough.

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