Geodesic
Existence and multiplicity of solutions for nonhomogeneous Klein-Gordon-Maxwell equations
Electronic Journal of Differential Equations, Tome 2015 (2015).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     author = {Xu, Liping and Chen, Haibo},
     title = {Existence and multiplicity of solutions for nonhomogeneous {Klein-Gordon-Maxwell} equations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2015},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a34/}
}
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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/