Kirchhoff–Hardy Fractional Problems with Lack of Compactness

Abstract

This paper deals with the existence and the asymptotic behavior of nontrivial solutions for some classes of stationary Kirchhoff problems driven by a fractional integro-differential operator and involving a Hardy potential and different critical nonlinearities. In particular, we cover the delicate degenerate case, that is, when the Kirchhoff function M is zero at zero. To overcome the difficulties due to the lack of compactness as well as the degeneracy of the models, we have to make use of different approaches.

Keywords

• stationary kirchhoff–dirichlet problems
• hardy coefficients
• critical nonlinearities
• variational methods
• 35j60
• 35r11
• 35j20
• 35s15