Variational approach for the Kirchhoff problem involving the p$$ p $$‐Laplace operator and the ψ$$ \psi $$‐Hilfer derivative

Abstract

This work aims to develop the variational framework for some Kirchhoff problems involving both the ‐Laplace operator and the ‐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 ‐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).