Remarks on a Class of Nonlinear Schrödinger Equations with Potential Vanishing at Infinity

Hongbo Zhu

Discrete Dynamics in Nature and Society, 2013, vol. 2013, 1-7

Abstract:

We study the following nonlinear Schrödinger equation , where the potential vanishes at infinity. Working in weighted Sobolev space, we obtain the ground states of problem under a Nahari type condition. Furthermore, if are radically symmetric with respect to , it is shown that problem has a positive solution with some more general growth conditions of the nonlinearity. Particularly, if , then the growth restriction in Ambrosetti et al. (2005) can be relaxed to , where if .

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:786736

DOI: 10.1155/2013/786736

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