Existence and multiplicity of solutions for Klein–Gordon–Maxwell systems with sign-changing potentials View Full Text


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Article Info

DATE

2019-12

AUTHORS

Chongqing Wei, Anran Li

ABSTRACT

In this paper, we study the following nonlinear Klein–Gordon–Maxwell system: {−Δu+V(x)u−(2ω+ϕ)ϕu=f(x,u)+λh(x)|u|q−2u,x∈R3,Δϕ=(ω+ϕ)u2,x∈R3,(Pλ) where ω and λ are positive constants, V is a continuous function with negative infimum, q∈(1,2), h∈L22−q(R3) is a positive potential function. Under the classic Ambrosetti–Rabinowitz condition, nontrivial solutions are obtained via the symmetric mountain pass theorem and the mountain pass theorem. In our paper, the nonlinearity F can also change sign and does not need to satisfy any 4-superlinear condition. We extend and improve some existing results to some extent. More... »

PAGES

72

References to SciGraph publications

  • 2010-10. Multiple solutions for nonhomogeneous Schrödinger–Maxwell and Klein– Gordon–Maxwell equations on R3 in NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS NODEA
  • 2014-04. Multiplicity of Solutions for a Nonlinear Klein-Gordon-Maxwell System in ACTA APPLICANDAE MATHEMATICAE
  • 2014-01. On perturbation of a functional with the mountain pass geometry in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
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    http://scigraph.springernature.com/pub.10.1186/s13662-019-2020-9

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