28 jan 2025 -- 15:00   [open in google calendar]

Abstract.

In this talk we will present results of existence and localization of solutions for nonlocal differential problems in abstract spaces. A focus will be given to techniques that allow weakening the classical compactness assumptions often found in the literature for studying differential equations in abstract spaces using topological methods, with an emphasis on a procedure based on fixed point theorems associated with the so-called transversality conditions. This technique provides a unifying method for studying models describing reaction-diffusion processes in several frameworks. We will consider nonlocal initial conditions such as the Cauchy multipoint and the mean value conditions, and we can handle nonlinearity with superlinear growth, for instance cubic polynomials or maps depending on the integral of the solution, thus encompassing nonlocal diffusion behaviours.