Construction of a topological degree theory for noncompact perturbations of zero-index Fredholm maps between Banach spaces. Study of various degree-related properties, such as the validity of a Borsuk-type odd map theorem. Definition of the concept of a one-point spectrum for continuous, nonlinear maps between Banach spaces. Applications of topological degree theory and fixed-point index theory to continuation problems. Study of delay differential equations on differentiable manifolds, with particular attention to the bifurcation of periodic solutions. Study of algebro-differential equations, with particular attention to the bifurcation of periodic solutions.
