Work

Multiplicity and Concentration of Solutions to a Singular Choquard Equation With Critical Sobolev Exponent

Year: 2025

Type: article

Abstract: In this paper, we consider a nonautonomous singular Choquard equation with critical exponent $ \left \{\begin{array}{lcl} -\Delta u+V(x)u+\lambda(I_\alpha\ast |u|^{p})|u|^{p-2}u=f(x)u^{-\gamma}+|u|^{4}u, &&\quad x\in\mathbb{R}^3,\\ u>0,&&\quad x\in\mathbb{R}^3, \end{array}\right. $ where $ I_\alpha $ is the Riesz potential of order $ \alpha\in(0,3) $ and $ 1+\frac{\alpha}{3}\le p<3 $, $ 0<\gamma<1 $. Under certain assumptions on $ V $ and $ f $, we show the existence and multiplicity of positive solutions for $ \lambda>0 $ by using variational method and Nehari type constraint. We also study concentration of solutions as $ \lambda\rightarrow0^+ $.

Source: Journal of Applied Analysis & Computation

DOI: 10.11948/20230439

Authors: Shengbin Yu, Jianqing Chen

Institutions: Fujian Business University, National Natural Science Foundation of China, Fujian Normal University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, Natural Science Foundation of Fujian Province

Awards: 约束临界点研究, G6398474901, G701624253