Geodesic
Existence and multiplicity of solutions for nonhomogeneous Klein-Gordon-Maxwell equations
Electronic journal of differential equations, Tome 2015 (2015)
This article concerns the nonhomogeneous Klein-Gordon-Maxwell equation

$\displaylines{ -\Delta u+u-(2\omega +\phi)\phi u=|u|^{p-1}u +h(x), \quad{in }\mathbb{R}^3,\cr \Delta \phi=(\omega +\phi)u^2,\quad{in }\mathbb{R}^3, }$

where $\omega>0$ is constant, $p\in(1,5)$. Under appropriate assumptions on $h(x)$, the existence of at least two solutions is obtained by applying the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory.
Classification : 35J20, 35J65, 35J60
Keywords: nonhomogeneous Klein-Gordon-Maxwell equations, multiple solutions, pohozaev identity, variational method 
@article{EJDE_2015__2015__a34,
     author = {Xu,  Liping and Chen,  Haibo},
     title = {Existence and multiplicity of solutions for nonhomogeneous {Klein-Gordon-Maxwell} equations},
     journal = {Electronic journal of differential equations},
     year = {2015},
     volume = {2015},
     zbl = {1315.35073},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a34/}
}
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JO  - Electronic journal of differential equations
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%A Chen,  Haibo
%T Existence and multiplicity of solutions for nonhomogeneous Klein-Gordon-Maxwell equations
%J Electronic journal of differential equations
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%F EJDE_2015__2015__a34
Xu,  Liping; Chen,  Haibo. Existence and multiplicity of solutions for nonhomogeneous Klein-Gordon-Maxwell equations. Electronic journal of differential equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a34/