Existence of solutions to the self-dual equations in the Maxwell gauged sigma model
The authors consider a self-dual Maxwell gauged \(O(3)\) sigma model. The existence of solutions for this model is proved by using the super and subsolution method. They obtain a subsolution by solving a Laplace equation on a weighted Sobolev space. The supersolutions are explicit constructed. Taking into account different values of a parameter which represents the decay rates of solutions at infinity, the subsolutions are given in different ways. So, if this parameter has noncritical values, the subsolutions are obtained via Laplace equation in Sobolev space, while if the above mentioned parameter is the critical number, the subsolutions are obtained via induction and shooting arguments.
scientific article; zbMATH DE number 5960910
scientific article