Ground state solutions for generalized quasilinear Schrödinger equations

Article type: Research Article

Authors: Fang, Xiang-Dong^{; *} | Han, Zhi-Qing

Affiliations: School of Mathematical Sciences, Dalian University of Technology, 116024 Dalian, PR China

Correspondence: [*] Corresponding author. E-mail: fangxd0401@dlut.edu.cn.

Abstract: In this paper we consider the generalized quasilinear Schrödinger equations −div(g2(u)∇u)+g(u)g′(u)|∇u|2+V(x)u=h(x,u),x∈RN, where V and h are periodic in xi, 1⩽i⩽N. By using variational methods, we prove the existence of ground state solutions, i.e., nontrivial solutions with least possible energy.

Keywords: Quasilinear Schrödinger equation, ground state solution, asymptotically linear, Nehari manifold

DOI: 10.3233/ASY-241913

Journal: Asymptotic Analysis, vol. 140, no. 1-2, pp. 109-122, 2024