Abstract
In this paper, we dedicate to studying the following semilinear Schrödinger systemequation*-Δu+V1(x)u=Fu(x,u,v)amp;mboxin~RN,r-Δv+V2(x)v=Fv(x,u,v)amp;mboxin~RN,ru,v∈H1(RN),endequation*where the potentialViare periodic inx,i=1,2, the nonlinearityFis allowed super-quadratic at somex∈RNand asymptotically quadratic at the otherx∈RN. Under a local super-quadratic condition ofF, an approximation argument and variational method are used to prove the existence of Nehari–Pankov type ground state solutions and the least energy solutions.
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More From: Electronic Journal of Qualitative Theory of Differential Equations
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