Remarks on a Class of Nonlinear Schrödinger Equations with Potential Vanishing at Infinity
Author
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-12-26
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
We study the following nonlinear Schrödinger equation −Δu+V(x)u=K(x)f(u), x∈ℝN, u∈H1(ℝN), where the potential V(x) vanishes at infinity.
Working in weighted Sobolev space, we obtain the ground states of problem (?) under a Nahari type condition.
Furthermore, if V(x),K(x) are radically symmetric with respect to x∈ℝN, it is shown that problem (?) has a positive solution with some more general growth conditions of the nonlinearity.
Particularly, if f(u)=up, then the growth restriction σ≤p≤N+2/N-2 in Ambrosetti et al.
(2005) can be relaxed to σ~≤p≤N+2/N-2, where σ~<σ if 0<β<α<2.
American Psychological Association (APA)
Zhu, Hongbo. 2013. Remarks on a Class of Nonlinear Schrödinger Equations with Potential Vanishing at Infinity. Discrete Dynamics in Nature and Society،Vol. 2013, no. 2013, pp.1-7.
https://search.emarefa.net/detail/BIM-498032
Modern Language Association (MLA)
Zhu, Hongbo. Remarks on a Class of Nonlinear Schrödinger Equations with Potential Vanishing at Infinity. Discrete Dynamics in Nature and Society No. 2013 (2013), pp.1-7.
https://search.emarefa.net/detail/BIM-498032
American Medical Association (AMA)
Zhu, Hongbo. Remarks on a Class of Nonlinear Schrödinger Equations with Potential Vanishing at Infinity. Discrete Dynamics in Nature and Society. 2013. Vol. 2013, no. 2013, pp.1-7.
https://search.emarefa.net/detail/BIM-498032
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-498032