We prove the existence of vortex local minimizers to Ginzburg-Landau functional with a global magnetic effect. A domain perturbating method is developed, which allows us to extend a local minimizer on a nonsimply connected superconducting material to the local minimizer with vortex on a simply connected material.
"Domain perturbation method and local minimizers to Ginzburg-Landau functional with magnetic effect." Abstr. Appl. Anal. 5 (2) 101 - 112, 2000. https://doi.org/10.1155/S1085337500000233