EXISTENCE RESULTS FOR SOME p-KIRCHHOFF PROBLEMS WITH ψ-HILFER FRACTIONAL DERIVATIVE

Abstract

In this paper, we investigate the existence of solutions to a [Formula: see text]-Kirchhoff problem involving the [Formula: see text]-Hilfer fractional derivative. Specifically, we reformulate the problem by analyzing the associated functional energy. We then construct three disjoint sets and demonstrate that the functional energy has a critical point in each of these sets. Finally, based on the definitions of these sets, we show that in the first set the solution is positive, in the second set the solution is negative, and in the third set, the solution changes sign.