ON THE ORIENTED DEGREE OF A CERTAIN CLASS OF PERTURBATIONS OF FREDHOLM MAPPINGS, AND ON BIFURCATION OF SOLUTIONS OF A NONLINEAR BOUNDARY-VALUE PROBLEM WITH NONCOMPACT PERTURBATIONS

The concept of oriented degree is extended to the class of mappings of the form f - g, where f is a proper Fredholm mapping of nonnegative i ndex and g a continuous f-compactly restrictable mapping. In the case when f is a Fredholm mapping of zero index and f and g are equivariant with respect to the action of the circle and the toms, formulas are o btained which express the degree of these mappings in terms of invaria nts of representations of the corresponding groups. An application to the investigation of the global behavior of a bifurcation branch of a certain nonlinear boundary value problem is given.