Nonlinear elliptic equation arising from gauge field theory and cosmology

Xinfu Chen, Stuart Hastings, J. Bryce McLeod, Yisong Yang

Research output: Contribution to journalArticlepeer-review


We study radially symmetric solutions of a nonlinear elliptic partial differential equation in R2 with critical Sobolev growth, i.e. the nonlinearity is of exponential type. This problem arises from a wide variety of important areas in theoretical physics including superconductivity and cosmology. Our results lead to many interesting implications for the physical problems considered. For example, for the self-dual Chern-Simons theory, we are able to conclude that the electric charge, magnetic flux, or energy of a non-topological N-vortex solution may assume any prescribed value above an explicit lower bound. For the Einstein-matter-gauge equations, we find a necessary and sufficient condition for the existence of a self-dual cosmic string solution. Such a condition imposes an obstruction for the winding number of a string in terms of the universal gravitational constant.

Original languageEnglish (US)
Pages (from-to)453-478
Number of pages26
JournalProceedings of The Royal Society of London, Series A: Mathematical and Physical Sciences
Issue number1928
StatePublished - 1994

ASJC Scopus subject areas

  • General Engineering


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