Geodesic
Multiple solutions for semilinear Schrödinger equations with electromagnetic potential
Electronic journal of differential equations, Tome 2016 (2016)
In this article, we consider the existence of infinitely many nontrivial solutions for the following semilinear Schrödinger equation with electromagnetic potential

$ \big(-i\nabla+A(x)\big)^2u+V(x)u=f(x,|u|)u,\quad{in } \mathbb{R}^N $

where i is the imaginary unit, V is the scalar (or electric) potential, A is the vector (or magnetic) potential. We establish the existence of infinitely many solutions via variational methods.
Classification : 58E05, 35J20
Keywords: semilinear Schrödinger equation, magnetic potential, variational methods 
@article{EJDE_2016__2016__a12,
     author = {Zhang,  Wen and Tang,  Xianhua and Zhang,  Jian},
     title = {Multiple solutions for semilinear {Schr\"odinger} equations with electromagnetic potential},
     journal = {Electronic journal of differential equations},
     year = {2016},
     volume = {2016},
     zbl = {1333.35028},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a12/}
}
TY  - JOUR
AU  - Zhang,  Wen
AU  - Tang,  Xianhua
AU  - Zhang,  Jian
TI  - Multiple solutions for semilinear Schrödinger equations with electromagnetic potential
JO  - Electronic journal of differential equations
PY  - 2016
VL  - 2016
UR  - http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a12/
LA  - en
ID  - EJDE_2016__2016__a12
ER  - 
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%A Zhang,  Wen
%A Tang,  Xianhua
%A Zhang,  Jian
%T Multiple solutions for semilinear Schrödinger equations with electromagnetic potential
%J Electronic journal of differential equations
%D 2016
%V 2016
%U http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a12/
%G en
%F EJDE_2016__2016__a12
Zhang,  Wen; Tang,  Xianhua; Zhang,  Jian. Multiple solutions for semilinear Schrödinger equations with electromagnetic potential. Electronic journal of differential equations, Tome 2016 (2016). http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a12/