Variational approach for the Kirchhoff problem involving the p-Laplace operator and the ?-Hilfer derivative

This work aims to develop the variational framework for some Kirchhoff problems involving both the p-Laplace operator and the Psi-Hilfer derivative. Precisely, we use the mountain pass theorem to prove the existence of nontrivial solutions. Moreover, the multiplicity of solutions is proved by the use of the Z(2)-symmetry mountain pass theorem. Our main results generalize the paper of Torres (J Fract Calculus Appli. 2014;5(1):1-10) and the work of Sousa et al. (Comp Appl Math. 2019;38:4).