| Abstract: |
| In this talk, we discuss about Kirchhoff type problems driven by nonlocal fractional operators, involving singular terms and critical Sobolev nonlinearities. In particular, we focus our attention on singular terms of type $u^\gamma$, with a negative exponent $\gamma$. Our variational problems present some difficulties due to the bi-nonlocal nature of the elliptic part, the nondifferentiability of the related functional and the lack of compactness at critical level. For this, in order to state existence and multiplicity results, we introduce different proof techniques based on approximation and minimization arguments. Finally, we present some interesting open questions, concerning the study of our problems. |
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