Periodic and asymptotically periodic quasilinear elliptic systems

Abstract

In this work, we are concerned with the existence and nonexistence of ground state solutions for the following class of quasilinear Schrödinger coupled systems taking into account periodic or asymptotically periodic potentials. The nonlinear terms are superlinear at infinity and at the origin. By using a change of variable, we turn the quasilinear system into a nonlinear system where we can establish a variational approach with a fine analysis on the Nehari method. For the nonexistence result, we compare the potentials with periodic potentials proving the nonexistence of ground state solutions.