The Existence of Infinitely Many Solutions for the Nonlinear Schrödinger–Maxwell Equations

In this paper, by using variational methods and critical point theory, we shall mainly be concerned with the study of the existence of infinitely many solutions for the following nonlinear Schrödinger–Maxwell equations - ▵ u + V ( x ) u + ϕ u = f ( x , u ) , in R 3 , - ▵ ϕ = u 2 , in R 3 , where the...

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Bibliographic Details
Published inResultate der Mathematik Vol. 65; no. 1-2; pp. 223 - 234
Main Authors Huang, Wen-nian, Tang, X. H.
Format Journal Article
LanguageEnglish
Published Basel Springer Basel 01.02.2014
Subjects
Mathematics
Mathematics and Statistics
variational methods
35J20
critical point
Schrödinger–Maxwell equations
35J25
35J60
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ISSN1422-6383
1420-9012
DOI10.1007/s00025-013-0342-6

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Summary:In this paper, by using variational methods and critical point theory, we shall mainly be concerned with the study of the existence of infinitely many solutions for the following nonlinear Schrödinger–Maxwell equations - ▵ u + V ( x ) u + ϕ u = f ( x , u ) , in R 3 , - ▵ ϕ = u 2 , in R 3 , where the potential V is allowed to be sign-changing, under some more assumptions on f , we get infinitely many solutions for the system.
ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-013-0342-6