Geodesic
Multiple solutions for Schrödinger-Maxwell systems with unbounded and decaying radial potentials
Electronic Journal of Differential Equations, Tome 2014 (2014).

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

Summary: 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__a41,
     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},
     publisher = {mathdoc},
     volume = {2014},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a41/}
}
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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__a41/