Ground state solution for the Schrödinger equation with Hardy potential and critical Sobolev exponent

Article type: Research Article

Authors: Zhang, Jing^a | Li, Lin^{b; *}

Affiliations: [a] Mathematics Sciences College, Inner Mongolia Normal University, Hohhot 010022, China. E-mail: [email protected] | [b] School of Mathematics and Statistics & Chongqing Key Laboratory of Social Economy and Applied Statistics, Chongqing Technology and Business University, Chongqing 400067, China. E-mails: [email protected], [email protected]

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

Abstract: In this paper, we consider the following Schrödinger equation (0.1)−Δu−μu|x|2+V(x)u=K(x)|u|2∗−2u+f(x,u),x∈RN,u∈H1(RN), where N⩾4, 0⩽μ<μ‾, μ‾=(N−2)24, V is periodic in x, K and f are asymptotically periodic in x, we take advantage of the generalized Nehari manifold approach developed by Szulkin and Weth to look for the ground state solution of (0.1).

Keywords: Schrödinger equation, generalized Nehari manifold, asymptotically periodic

DOI: 10.3233/ASY-211737

Journal: Asymptotic Analysis, vol. 129, no. 3-4, pp. 485-503, 2022