The fixed point index enjoys a number of properties whose precise statement may vary in the literature. The prominent ones are those of normalization, additivity, homotopy invariance, commutativity,… (More)

Given a tangent vector field on a finite-dimensional real smooth manifold, its degree also known as characteristic or rotation is, in some sense, an algebraic count of its zeros and gives useful… (More)

Is the one-to-one continuous image of an open set in R still open? This problem is the so called invariance of domain and, as H. Freudenthal pointed out in his essay on the history of topology [6]… (More)

Let T be a selfadjoint bounded operator acting in a real Hilbert space H, and denote by S the unit sphere of H. Assume that λ0 is an isolated eigenvalue of T of odd multiplicity greater than 1. Given… (More)

We consider T -periodic parametrized retarded functional differential equations, with infinite delay, on (possibly) noncompact manifolds. Using a topological approach, based on the notions of degree… (More)

Let T be a selfadjoint bounded operator acting in a real Hilbert space H, and denote by S the unit sphere of H. Assume that λ0 is an isolated eigenvalue of T of odd multiplicity greater than 1. Given… (More)

where λ ≥ 0 is a real parameter. We deal with the problem of the existence of T -periodic solutions of (1.1), with a special attention to the case of small values of λ. Clearly, when λ = 0, any point… (More)