ABSTRACT

Recently, a great attention has been drawn to the study of fractional and nonlocal operators of elliptic type. These operator arise in a quite natural way in many different applications, such as, continuum mechanics, phase transition phenomena, population dynamic and game theory, as they are typical outcome of stochastically stabilization of Levy processes.

The talk is focused on recent results concerning existence, multiplicity and asymptotic behavior of positive solutions of some Kirchhoff type problems, involving fractional integro-differential elliptic operators and presenting also difficulties due to intrinsic lacks of compactness, which arise from different reasons. The problems presented are highly nonlocal because of the presence of the fractional integro-differential elliptic operators and of the Kirchhoff coefficients. The proof techniques should therefore overcome the nonlocal nature of the problems as well as the lack of compactness, and the suitable strategies adopted depend of course on the problem under consideration.

[Light refreshments will be served outside the venue at 4:00-4:30 pm. Please come and join us.]