Ground state solutions for quasilinear Schrodinger equations with periodic potential

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.

Keywords

• quasilinear schrodinger equation
• nehari manifold
• ground state