Hokkaido Mathematical Journal

SHIRAI Shin-ichi,

Existence and decay of solutions to a semilinear Schrödinger equation with magnetic field.

Hokkaido Mathematical Journal, 37 (2008) pp.241-273

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Abstract

In this paper we study the decay property of solutions of a semilinear Schrödinger equation, $-(∇ - iA)^{2}u+(V-E)u=Q|u|^{p-2}u$, on $\mathbb R^{n}$, where $n \geq 2$ and $2

MSC(Primary)35J60
MSC(Secondary)35B40, 35J10
Uncontrolled KeywordsGaussian decay of stationary solutions, nonlinear Schr\"{o}dinger equation, magnetic field