## Abstract

We study radially symmetric solutions of a nonlinear elliptic partial differential equation in R^{2} 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 language | English (US) |
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Pages (from-to) | 453-478 |

Number of pages | 26 |

Journal | Proceedings of The Royal Society of London, Series A: Mathematical and Physical Sciences |

Volume | 446 |

Issue number | 1928 |

DOIs | |

State | Published - 1994 |

## ASJC Scopus subject areas

- Engineering(all)