Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 82, pp. 1-12.

Title: Ground state solutions for quasilinear Schrodinger equations with periodic potential
       
Authors: Jing Zhang (Inner Mongolia Normal Univ., Hohhot, China)
         Chao Ji (East China Univ. of Science and Tech., Shanghai, China)

Abstract:
 This article concerns the  quasilinear Schrodinger equation
 $$\displaylines{
 -\Delta u-u\Delta (u^2)+V(x)u=K(x)|u|^{2\cdot2^*-2}u+g(x,u),\quad  x\in\mathbb{R}^N, \cr
 u\in H^1(\mathbb{R}^N),\quad u>0,
 }$$
 where V and K are positive, continuous and periodic functions,
 g(x,u) is periodic in x and has subcritical growth.
 We use the generalized Nehari  manifold approach developed by Szulkin and Weth
 to study the ground state solution, i.e. the nontrivial solution with least
 possible energy.
 
Submitted March 11, 2020. Published July 29, 2020.
Math Subject Classifications: 35A15, 35B33, 35B38.
Key Words: Quasilinear Schrodinger equation; Nehari manifold; ground state.