| Abstract: |
| We consider the following class of fractional Schr\odinger equations
$$
(-\Delta)^{s} u + V(x)u = K(x) f(u) \mbox{ in } \R^{N}
$$
where $s\in (0, 1)$, $N>2s$, $(-\Delta)^{s}$ is the fractional Laplacian, the potentials $V, K$ are positive and continuous functions allowed for vanishing behavior at infinity, and $f$ is a subcritical continuous function. By using a minimization argument and a quantitative deformation lemma, we obtain the existence of a sign-changing solution. Moreover, when $f$ is odd, the problem admits infinitely many nontrivial solutions (not necessarily sign-changing). |
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