Geodesic
Multiple solutions for semilinear Schrödinger equations with electromagnetic potential
Electronic Journal of Differential Equations, Tome 2016 (2016).

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Summary: 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__a45,
     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},
     publisher = {mathdoc},
     volume = {2016},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a45/}
}
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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__a45/