18 sep 2024 -- 16:30   [open in google calendar]

SNS, Aula Volterra

Abstract.

In 1897, Kirchhoff introduced a model aimed at generalizing the well-known d'Alembert equation by also incorporating lateral displacement. Over the years, Kirchhoff's equation has been extended in various directions, as it proved capable of modeling a wide range of phenomena. In this talk, we will present some recent existence results for a non-local, nonlinear version of the Kirchhoff equation, driven by the fractional p-Laplacian and featuring a critical term in the sense of the Sobolev exponent on the right-hand side. These results can be viewed as an extension of those published by Brezis and Nirenberg in their seminal 1983 paper.