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Zbl 1205.35099
Moschetto, Danila Sandra
Existence and multiplicity results for a nonlinear stationary Schrödinger equation. (English)
[J] Ann. Pol. Math. 99, No. 1, 39-43 (2010). ISSN 0066-2216; ISSN 1730-6272/e

Summary: We revisit Kristály's result on the existence of weak solutions of the Schrödinger equation of the form $$ -\Delta u+a(x)u=\lambda b(x)f(u), \quad x\in\Bbb R^N,\ u\in H^1(\Bbb R^N), $$ where $\lambda$ is a positive parameter, $a$ and $b$ are positive functions, while $f:\Bbb R\rightarrow\Bbb R$ 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.

MSC 2000:: *35J61
35J20 Second order elliptic equations, variational methods
35B45 A priori estimates

Keywords: nonlinear stationary Schrödinger equations; multiple solutions

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