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

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.