Hokkaido Mathematical Journal

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

Shin-ichi SHIRAI

Full-text: Open access

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.

Article information

Source
Hokkaido Math. J., Volume 37, Number 2 (2008), 241-273.

Dates
First available in Project Euclid: 21 September 2009

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1253539554

Digital Object Identifier
doi:10.14492/hokmj/1253539554

Mathematical Reviews number (MathSciNet)
MR2415900

Zentralblatt MATH identifier
1144.35048

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B40: Asymptotic behavior of solutions 35J10: Schrödinger operator [See also 35Pxx]

Keywords
Gaussian decay of stationary solutions nonlinear Schr\"{o}dinger equation magnetic field

Citation

SHIRAI, Shin-ichi. Existence and decay of solutions to a semilinear Schrödinger equation with magnetic field. Hokkaido Math. J. 37 (2008), no. 2, 241--273. doi:10.14492/hokmj/1253539554. https://projecteuclid.org/euclid.hokmj/1253539554


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