Analysis of a semilinear pde for modeling static solutions of Josephson junctions

A semilinear elliptic partial differential equation problem that models the static (zero voltage) behavior of a Josephson window junction is considered. A priori estimates and differential properties of the solution are obtained. The existence of the solutions is shown and iterative methods for solving this problem are analyzed. Experimental numerical data that couple with the theoretical results are presented. Useful physical information is extracted from our analysis