Concentrating solutions of the fractional (p,q)-Choquard equation with exponential growth

2025/05/31 by Song, Yueqiang, Sun, Xueqi, Repovš, Dušan D.
#35A15 #35A23 #35J35 #35J60 #35R11 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.00412

Abstract

This article deals with the following fractional (p,q)-Choquard equation with exponential growth of the form: ε^ps(-Δ)_p^su+ε^qs(-Δ)_q^su+ Z(x)(|u|^p-2u+|u|^q-2u)=ε^μ-N[|x|^-μ*F(u)]f(u) in ℝ^N, where s∈ (0,1), ε>0 is a parameter, 2≤ p=(N)/(s)0 small enough. In a certain sense, we generalize some previously known results.

Citations

• Semi-classical states for the nonlinear Choquard equations: existence, multiplicity and concentration at a potential well
• On the Moser-Trudinger inequality in fractional Sobolev-Slobodeckij spaces
• Hitchhiker's guide to the fractional Sobolev spaces
• Hitchhikerʼs guide to the fractional Sobolev spaces
• Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation

Related

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• Normalized solutions for fractional Choquard equation with critical growth on bounded domain
• Semi-classical states for fractional Choquard equations with decaying potentials
• On the existence of normalized solutions to a class of fractional Choquard equation with potentials
• The Choquard logarithmic equation involving fractional Laplacian operator and a nonlinearity with exponential critical growth