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This paper is concerned with the following Klein-Gordon-Maxwell system: $$ \left\{ \begin{array}{ll} \displaystyle -\Delta u+\lambda V(x)u-(2\omega+\phi)\phi u=f(x,u), \mbox{ \ \ }x\in\mathbb{R}^{3},\\ \Delta\phi=(\omega+\phi)u^{2},\mbox{ \ \ }x\in\mathbb{R}^{3}, \end{array} \right. $$ 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.
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참고문헌 (19)
참고문헌 신청
A. Azzollini / 2010 / Ground state solutions for the nonlinear Klein-Gordon-Maxwell equations / Topol. Methods Nonlinear Anal 35 (1) : 33 ~ 42
A. Azzollini / 2011 / Impoved estimates and a limit case for the electrostatic Klein-Gordon-Maxwell system / Proc. R. Soc. Edinb. Sect. A 141 (3) : 449 ~ 463
D. Cassani / 2004 / Existence and non-existence of solitary waves for the critical Klein-Gordon-Maxwell equation coupled with Maxwell’s equations / Nonlinear Anal 58 (7-8) :
F. Z.Wang / 2011 / Solitary waves for the Klein-Gordon-Maxwell system with critical exponent / Nonlinear Anal 74 : 827 ~ 835
I. Ekeland / 1990 / Convexity Methods in Hamiltonian Mechanics / Springer
A. Azzollini / 2011 / Impoved estimates and a limit case for the electrostatic Klein-Gordon-Maxwell system / Proc. R. Soc. Edinb. Sect. A 141 (3) : 449 ~ 463
D. Cassani / 2004 / Existence and non-existence of solitary waves for the critical Klein-Gordon-Maxwell equation coupled with Maxwell’s equations / Nonlinear Anal 58 (7-8) :
F. Z.Wang / 2011 / Solitary waves for the Klein-Gordon-Maxwell system with critical exponent / Nonlinear Anal 74 : 827 ~ 835
I. Ekeland / 1990 / Convexity Methods in Hamiltonian Mechanics / Springer
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