Sign-changing ground state solutions for discrete nonlinear Schrödinger equations

Abstract

ABSTRACTIn this paper, we study the existence of least energy sign-changing solutions and ground state solutions for the discrete nonlinear Schrödinger equation where is a sequence of positive numbers, is a constant. By using variational and some new analytic techniques, we prove that the above equation possesses one ground state solution and one least energy sign-changing solution, which changes sign exactly once. Furthermore, we show that the energy of the sign-changing solution is larger than twice the ground state energy. Our results strongly extend and complement the known ones in the literature.