Standing waves for nonlinear Schrödinger equations with singular potentials
Jaeyoung Byeon
Department of Mathematics, POSTECH, San 31 Hyoja-dong, Nam-gu, Pohang, Kyungbuk 790-784, Republic of KoreaZhi-Qiang Wang
Department of Mathematics and Statistics, Utah State University, Logan, UT 84322, USA
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Abstract
We study semiclassical states of nonlinear Schrödinger equations with anisotropic type potentials which may exhibit a combination of vanishing and singularity while allowing decays and unboundedness at infinity. We give existence of spike type standing waves concentrating at the singularities of the potentials.
Résumé
Nous étudions les états semi-classiques des équations de Schrödinger non linéaires avec potentiels de type anisotropiques qui peuvent tendre vers zéro à l'infini, pour lesquels des phénomènes d'évanescence et de singularité sont possibles. Nous donnons l'existence d'ondes stationnaires se concentrant aux singularités des potentiels.
Cite this article
Jaeyoung Byeon, Zhi-Qiang Wang, Standing waves for nonlinear Schrödinger equations with singular potentials. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 3, pp. 943–958
DOI 10.1016/J.ANIHPC.2008.03.009