Ground state solutions for quasilinear Schrodinger equations with periodic potential

Abstract

This article concerns the quasilinear Schrödinger equation -Δu - uΔ(u2) + V(x)u = K(x)|u|2‧2*-2u + g(x, u), x ∈ ℝN, u ∈ H1(ℝN), 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.