Boundary value problems of the Ginzburg–Landau equations
Yisong Yang · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1990
Synopsis For a domain Ω in the Euclidean space R d (d = 2, 3) existence of weak solutions for both interior and exterior Dirichlet boundary value problems of the Ginzburg-Landau equations are established without any restriction on the range of the coupling constant λ, thesize of Ω, or the boundary data. For the critical choice λ = 1, we prove the existence of confined multivortices in a bounded domain by a constructive monotone iteration method.