Existence and Multiplicity of Solutions for Sublinear Schrödinger Equations with Coercive Potentials
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-08-27
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
In this study, we consider the following sublinear Schrödinger equations −Δu+Vxu=fx,u,for x∈ℝN,ux⟶0,asu⟶∞, where fx,u satisfies some sublinear growth conditions with respect to u and is not required to be integrable with respect to x.
Moreover, V is assumed to be coercive to guarantee the compactness of the embedding from working space to LpℝN for all p∈1,2∗.
We show that the abovementioned problem admits at least one solution by using the linking theorem, and there are infinitely many solutions when fx,u is odd in u by using the variant fountain theorem.
American Psychological Association (APA)
Wu, Dong-Lun. 2019. Existence and Multiplicity of Solutions for Sublinear Schrödinger Equations with Coercive Potentials. Mathematical Problems in Engineering،Vol. 2019, no. 2019, pp.1-8.
https://search.emarefa.net/detail/BIM-1198057
Modern Language Association (MLA)
Wu, Dong-Lun. Existence and Multiplicity of Solutions for Sublinear Schrödinger Equations with Coercive Potentials. Mathematical Problems in Engineering No. 2019 (2019), pp.1-8.
https://search.emarefa.net/detail/BIM-1198057
American Medical Association (AMA)
Wu, Dong-Lun. Existence and Multiplicity of Solutions for Sublinear Schrödinger Equations with Coercive Potentials. Mathematical Problems in Engineering. 2019. Vol. 2019, no. 2019, pp.1-8.
https://search.emarefa.net/detail/BIM-1198057
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1198057