Solutions to a gauged Schrödinger equation with concave–convex nonlinearities without (AR) condition

Abstract

In this paper, we are concerned with a gauged nonlinear Schrödinger equation where are positive parameters and Under appropriate assumptions on the potential V and nonlinear terms g and f, where g has sublinear growth and f has asymptotically linear or superlinear growth without (AR) condition, we acquire the existence and multiplicity of solutions by means of Mountain pass theorem and Fountain theorem. Our results generalize and improve the recent result in the literature.