A Bifurcation of Solutions of Operator Equations in Spaces with Metric

In the present paper branching of solutions of operator equations of the specific kind (which are applied in quantum transport theory) in complete metrizable spaces is investigated. The possibility of increasing Fredholm operator kernel dimension for post-critical values of parameter argument is analyzed. For the case of weakly continuous perturbations of this map local existence of two branches of equation which connected with summary operator is demonstrated.