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Infinitely many solutions for a class of sublinear fractional Schrödinger equations with indefinite potentials. (English) Zbl 1503.35260

Summary: In this paper, we consider the following sublinear fractional Schrödinger equation: \[ (-\Delta)^su + V(x)u= K(x) \vert u \vert^{p-1}u,\quad x\in \mathbb{R}^N,\] where \(s, p\in(0,1)\), \(N>2s\), \((-\Delta)^s\) is a fractional Laplacian operator, and \(K\), \(V\) both change sign in \(\mathbb{R}^N \). We prove that the problem has infinitely many solutions under appropriate assumptions on \(K\), \(V\). The tool used in this paper is the symmetric mountain pass theorem.

MSC:

35R11 Fractional partial differential equations
35Q55 NLS equations (nonlinear Schrödinger equations)
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