• 제목/요약/키워드: Sobolev-type embedding

검색결과 3건 처리시간 0.019초

EXISTENCE AND MULTIPLICITY OF NONTRIVIAL SOLUTIONS FOR KLEIN-GORDON-MAXWELL SYSTEM WITH A PARAMETER

  • Che, Guofeng;Chen, Haibo
    • 대한수학회지
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    • 제54권3호
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    • pp.1015-1030
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    • 2017
  • This paper is concerned with the following Klein-Gordon-Maxwell system: $$\{-{\Delta}u+{\lambda}V(x)u-(2{\omega}+{\phi}){\phi}u=f(x,u),\;x{\in}\mathbb{R}^3,\\{\Delta}{\phi}=({\omega}+{\phi})u^2,\;x{\in}\mathbb{R}^3$$ where ${\omega}$ > 0 is a constant and ${\lambda}$ is the parameter. Under some suitable assumptions on V (x) and f(x, u), we establish the existence and multiplicity of nontrivial solutions of the above system via variational methods. Our conditions weaken the Ambrosetti Rabinowitz type condition.