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May 2008 Existence and decay of solutions to a semilinear Schrödinger equation with magnetic field
Shin-ichi SHIRAI
Hokkaido Math. J. 37(2): 241-273 (May 2008). DOI: 10.14492/hokmj/1253539554

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 $2<p <2^{*}$. We give a lower bound estimate of nontrivial solutions at infinity. In two-dimensional case, we give super-exponential decay estimates of solutions at infinity. Moreover, we show the existence of a nontrivial solution under additional assumptions on potentials.

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Shin-ichi SHIRAI. "Existence and decay of solutions to a semilinear Schrödinger equation with magnetic field." Hokkaido Math. J. 37 (2) 241 - 273, May 2008. https://doi.org/10.14492/hokmj/1253539554

Information

Published: May 2008
First available in Project Euclid: 21 September 2009

zbMATH: 1144.35048
MathSciNet: MR2415900
Digital Object Identifier: 10.14492/hokmj/1253539554

Subjects:
Primary: 35J60
Secondary: 35B40, 35J10

Rights: Copyright © 2008 Hokkaido University, Department of Mathematics

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Vol.37 • No. 2 • May 2008
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