Ground state solutions for nonlinear Choquard equations with inverse-square potentials¹

Article type: Research Article

Authors: Guo, Ting | Tang, Xianhua^{; *}

Affiliations: School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, P.R. China. E-mails: [email protected], [email protected]

Correspondence: [*] Corresponding author. E-mail: [email protected].

Note: [1] This work is partially supported by the NNFC (No: 11571370, 11471137) of China.

Abstract: This paper is concerned with the following Choquard equation −Δu+(V(x)−μ|x|2)u=(∫RNF(u(y))|x−y|αdy)f(u),u∈H1(RN), where N⩾3, 0⩽μ<(N−2)24, 0<α<N, V is 1-periodic in each of x1,x2,…,xN and F is the primitive function of f. Under some mild assumptions on V and f, we establish the existence and asymptotical behavior of ground state solutions by variational methods.

Keywords: Choquard equation, ground state solutions, asymptotical behavior, inverse square potential

DOI: 10.3233/ASY-191549

Journal: Asymptotic Analysis, vol. 117, no. 3-4, pp. 141-160, 2020