Existence and concentration of ground states for saturable nonlinear Schrödinger equations with intensity functions in [formula omitted

Abstract

In this paper, we study the existence and concentration behavior of semiclassical ground states for a class of saturable nonlinear Schrödinger equations with intensity functions in R2: (0.1)−ε2Δv+ΓI(x)+v21+I(x)+v2v=λv,forx∈R2.We show that for sufficiently negatively large coupling constant Γ and sufficiently small ε there exists a family of normalized ground states (i.e., with the L2 constraint) of the problem. We prove that the family of solutions concentrate around the maxima of the intensity function as ε→0. Our method is variational and depends upon a convexity technique together with the concentration-compactness method.