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Multiplicity of solutions for Schrödinger equations with concave-convex nonlinearities. (English) Zbl 1357.35102

Summary: We study the multiplicity of solutions for a class of semilinear Schrödinger equations: \(- \Delta u + V(x) u = g (x, u)\), for \(x \in \mathbb{R}^N\); \(u(x) \rightarrow 0\), as \(|u| \rightarrow \infty\), where \(V\) satisfies some kind of coercive condition and \(g\) involves concave-convex nonlinearities with indefinite signs. Our theorems contain some new nonlinearities.

MSC:

35J10 Schrödinger operator, Schrödinger equation
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