AN IMPROVED RESULT ON GROUND STATE SOLUTIONS OF QUASILINEAR SCHRÖDINGER EQUATIONS WITH SUPER-LINEAR NONLINEARITIES

Abstract

By using variational and some new analytic techniques, we prove the existence of ground state solutions for the quasilinear Schrödinger equation with variable potentials and super-linear nonlinearities. Moreover, we establish a minimax characterisation of the ground state energy. Our result improves and extends the existing results in the literature.