A perturbed fractional p-Kirchhoff problem with critical nonlinearity.

Seminario de Ecuaciones

Speaker: Luigi Appolloni, Università di Milano

Abstract: In this talk we are going to see some recent results obtained for a problem driven by the fractional $p$-laplacian coupled with a Kirchhoff type coefficient and a critical nonlinearity. Firstly we will explain how to prove the sequentially weakly lower semicontinuity of the energy functional associated with the problem and the validity of the Palais-Smale condition. After that, using variational methods and analysing the fiber maps of the energy functional, we will show the existence of a global minimizer and a mountain pass solution.