Existence and multiplicity of non-trivial solutions for a class of modified Schrödinger equation with non-coercive potential

In the present paper, we study the following modified nonlinear Schrödinger equation-▵u+V(x)u-12u▵u2=|u|p-1u+h(x),x∈RN,(P)where N⩾3,4⩽p+1<22∗N⩾3,4⩽p+1<22∗, h∈L2(RN)h∈L2(RN) and h≠0. Under some hypotheses on V, we obtain the existence and multiplicity of non-trivial solutions.