On ground state for a class of nonlinear Schrödinger equation

Abstract

I study the existence of ground state for the following periodic Schrödinger equation under the circumstance that the nonlinear term satisfies odd conditions by using the Mountain Pass Lemma and variational method. $$-\Delta u+V(x)u-\Delta(1+u^2)^{{1}/{2}}{u\over 2(1+u^2)^{{1}/{2}}}=f\,(x, u).$$

Keywords

• Schrödinger equation
• Mountain pass theorem
• variational method
• the existence of solutions