## Differential and Integral Equations

### Existence of non-topological solutions for a nonlinear elliptic equation arising from Chern-Simons-Higgs theory in a general background metric

Kazuhiro Kurata

#### Abstract

In this paper we show the existence of non-topological 0-vortex and 1-vortex solutions for a nonlinear elliptic equation arising from Chern-Simons-Higgs theory in a general background metric $(g_{\mu\nu})=diag(1, -k(x), -k(x))$ with decay $k(x)=O(|x|^{-l})$ for some $l >2$ at infinity.

#### Article information

Source
Differential Integral Equations, Volume 14, Number 8 (2001), 925-935.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356123173

Mathematical Reviews number (MathSciNet)
MR1827096

Zentralblatt MATH identifier
1027.35022

#### Citation

Kurata, Kazuhiro. Existence of non-topological solutions for a nonlinear elliptic equation arising from Chern-Simons-Higgs theory in a general background metric. Differential Integral Equations 14 (2001), no. 8, 925--935. https://projecteuclid.org/euclid.die/1356123173