Affiliations: [a] Mathematics Sciences College, Inner Mongolia Normal University, Hohhot 010022, China. E-mail: jinshizhangjing@163.com | [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: linli@ctbu.edu.cn, lilin420@gmail.com
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).
