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We consider the semilinear Schrödinger equation { −4 u+ V (x)u = f(x, u), x ∈ RN , u ∈ H1(RN ), where V (x) is asymptotically periodic and sign-changing, f(x, u) is a superlinear, subcritical nonlinearity. Under asymptotically periodic V (x) and a super-quadratic condition about f(x, u). We prove that the above problem has a ground state solution which minimizes the corresponding energy among all nontrivial solutions. c ©2016 All rights reserved.

Ground state solutions for an asymptotically periodic and superlinear Schrodinger equation