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We consider the semilinear Schrödinger equation −∆ A u + V (x)u = Q(x)|u| 2 * −2 u. Assuming that V changes sign, we establish the existence of a solution u = 0 in the Sobolev space H 1 A,V + (R N). The solution is obtained by a min-max type argument based on a topological linking. We also establish certain regularity properties of solutions for a rather general class of equations involving the operator −∆ A .

Abstract. We consider the semilinear Schrödinger equation

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