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Abstract

We revisit Kristály's result on the existence of weak solutions of the Schrödinger equation of the form $$ -{\mit\Delta} u+a(x)u=\lambda b(x)f(u), \quad\ x\in\mathbb{R}^N,\, u\in H^1(\mathbb{R}^N), $$ where $\lambda$ is a positive parameter, $a$ and $b$ are positive functions, while $f:\mathbb{R}\rightarrow\mathbb{R}$ is sublinear at infinity and superlinear at the origin. In particular, by using Ricceri's recent three critical points theorem, we show that, under the same hypotheses, a much more precise conclusion can be obtained.