Standing waves for a system of nonlinear Schrödinger equations in RN

In this paper we study the existence of bound state solutions for stationary Schrodinger systems of the form � −�u + V( x)u= K(x)Fu(u, v) in R N , −�v + V( x)v= K(x)Fv(u, v) in R N , where N 3, V and K are bounded continuous nonnegative functions, and F( u, v)is a C 1 and p-homogeneous function with 2 <p< 2N/(N − 2). We give a special attention to the case when V may eventually vanishes. Our arguments are based on penalization techniques, variational methods and Moser iteration scheme.

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