Min-max method for some classes of Kirchhoff problems involving the $ \psi $-Hilfer fractional derivative

In this work, we develop some variational settings related to some singular $ p $-Kirchhoff problems involving the $ \psi $-Hilfer fractional derivative. More precisely, we combine the variational method with the min-max method in order to prove the existence of nontrivial solutions for the given problem. Our main result generalizes previous ones in the literature.