Existence and multiplicity results for a nonlinear stationary Schrödinger equation

Danila Sandra Moschetto¹

¹ Department of Mathematics and Computer Science University of Catania Viale A. Doria, 6 95125 Catania, Italy

Annales Polonici Mathematici, Tome 99 (2010) no. 1, pp. 39-43

Résumé

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.

Détail

DOI : 10.4064/ap99-1-3

Keywords: revisit krist lys result existence weak solutions schr dinger equation form mit delta u lambda u quad mathbb mathbb where lambda positive parameter positive functions while mathbb rightarrow mathbb sublinear infinity superlinear origin particular using ricceris recent three critical points theorem under hypotheses much precise conclusion obtained