The paper studies existence of solutions for the nonlinear Schrödinger equation −(∇+iA(x))2u+V(x)u=f(|u|)u with a general bounded external magnetic field. In particular, no lattice periodicity of the magnetic field or presence of external electric field is required. Solutions are obtained by means of a general structural statement about bounded sequences in the magnetic Sobolev space.
Nonlinear Schrödinger equation with bounded magnetic field
Giuseppe Devillanova;
2020-01-01
Abstract
The paper studies existence of solutions for the nonlinear Schrödinger equation −(∇+iA(x))2u+V(x)u=f(|u|)u with a general bounded external magnetic field. In particular, no lattice periodicity of the magnetic field or presence of external electric field is required. Solutions are obtained by means of a general structural statement about bounded sequences in the magnetic Sobolev space.File in questo prodotto:
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