Multiple solutions for superlinear Klein–Gordon–Maxwell equations

In this paper, we consider the following Klein–Gordon–Maxwell equations −Δu+V(x)u−(2ω+ϕ)ϕu=f(x,u)+h(x)inR3,−Δϕ+ϕu2=−ωu2inR3,where ω>0 is a constant, u, ϕ:R3→R, V:R3→R is a potential function. By assuming the coercive condition on V and some new superlinear conditions on f, we obtain two nontrivia...

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Bibliographic Details
Published inMathematische Nachrichten Vol. 293; no. 9; pp. 1827 - 1835
Main Authors Wu, Dong‐Lun, Lin, Hongxia
Format Journal Article
LanguageEnglish
Published Weinheim Wiley Subscription Services, Inc 01.09.2020
Subjects
Coercivity
Klein–Gordon–Maxwell equations
Mathematical analysis
Maxwell's equations
multiple solutions
superlinear conditions
variational methods
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Summary:In this paper, we consider the following Klein–Gordon–Maxwell equations −Δu+V(x)u−(2ω+ϕ)ϕu=f(x,u)+h(x)inR3,−Δϕ+ϕu2=−ωu2inR3,where ω>0 is a constant, u, ϕ:R3→R, V:R3→R is a potential function. By assuming the coercive condition on V and some new superlinear conditions on f, we obtain two nontrivial solutions when h is nonzero and infinitely many solutions when f is odd in u and h≡0 for above equations.
Bibliography:D.‐L. Wu was partially supported by NSF of China (No. 11801472) and the Youth Science and Technology Innovation Team of Southwest Petroleum University for Nonlinear Systems (No. 2017CXTD02) and The Science and Technology Innovation Team of Education Department of Sichuan for Dynamical System and its Applications (No. 18TD0013). H. X. Lin was partially supported by the NSF of China (No. 11701049), the China Postdoctoral Science Foundation (No. 2017M622989), and the Scientific fund of the Education Department of Sichuan Province (No. 18ZB0069).
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.201900129