On Coincidence Index for Multivalued Perturbations of Nonlinear Fredholm Maps and Some Applications

One of the most efficient methods for the study of boundary and periodic problems for nonlinear differential equations and inclusions, consists in the operator treatment of these problems in suitable functional spaces. However, for a number of problems of this sort, the maps constructed in functional spaces do not possess “nice” properties on the whole domain, but only on some open neighborhood of the solutions set. As an example, we may note a Monge-Ampere problem arising in geometry of surfaces (see [10]). Moreover, the application of topological methods to the investigation of this kind of problems often requires the embedding of a given equation or inclusion into a corresponding parametric family. In such a situation, either solutions sets or their neighborhoods can vary in dependence of parameters. In the present paper, we want to study an inclusion of the form