Geodesic
Multiple solutions for Schrödinger-Maxwell systems with unbounded and decaying radial potentials
Electronic journal of differential equations, Tome 2014 (2014)
This article concerns the nonlinear Schrodinger-Maxwell system

$\displaylines{ -\Delta u +V(|x|)u +Q(|x|)\phi u=Q(|x|) f(u),\quad \hbox{in } \mathbb{R}^3\cr -\Delta \phi =Q(|x|) u^{2}, \quad \hbox{in } \mathbb{R}^3 }$

where V and Q are unbounded and decaying radial. Under suitable assumptions on nonlinearity $f(u)$, we establish the existence of nontrivial solutions and a sequence of high energy solutions in weighted Sobolev space via Mountain Pass Theorem and symmetric Mountain Pass Theorem.
Classification : 35J20, 35J60
Keywords: Schrödinger-Maxwell system, unbounded or decaying potential, weighted Sobolev space, mountain pass theorem 
@article{EJDE_2014__2014__a141,
     author = {Liao,  Fangfang and Wang,  Xiaoping and Liu,  Zhigang},
     title = {Multiple solutions for {Schr\"odinger-Maxwell} systems with unbounded and decaying radial potentials},
     journal = {Electronic journal of differential equations},
     year = {2014},
     volume = {2014},
     zbl = {1298.35075},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a141/}
}
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AU  - Wang,  Xiaoping
AU  - Liu,  Zhigang
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JO  - Electronic journal of differential equations
PY  - 2014
VL  - 2014
UR  - http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a141/
LA  - en
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%A Wang,  Xiaoping
%A Liu,  Zhigang
%T Multiple solutions for Schrödinger-Maxwell systems with unbounded and decaying radial potentials
%J Electronic journal of differential equations
%D 2014
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%U http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a141/
%G en
%F EJDE_2014__2014__a141
Liao,  Fangfang; Wang,  Xiaoping; Liu,  Zhigang. Multiple solutions for Schrödinger-Maxwell systems with unbounded and decaying radial potentials. Electronic journal of differential equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a141/