Affiliation:
1. Mathematics Sciences College, Inner Mongolia Normal University, Hohhot 010022, China. E-mail: jinshizhangjing@163.com
2. School of Mathematics and Statistics & Chongqing Key Laboratory of Social Economy and Applied Statistics, Chongqing Technology and Business University, Chongqing 400067, China. E-mails: linli@ctbu.edu.cn, lilin420@gmail.com
Abstract
In this paper, we consider the following Schrödinger equation (0.1) − Δ u − μ u | x | 2 + V ( x ) u = K ( x ) | u | 2 ∗ − 2 u + f ( x , u ) , x ∈ R N , u ∈ H 1 ( R N ) , where N ⩾ 4, 0 ⩽ μ < μ ‾, μ ‾ = ( N − 2 ) 2 4 , 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).