Existence and multiplicity results for Kirchhoff-type superlinear problems involving the fractional p(x)-Laplacian satisfying (C)-condition

Abstract

Our focus in this study revolves around investigating a Kirchhoff problem involving the fractional p(x)-Laplacian operator. The purpose is to study the existence and multiplicity of weak solutions for the above problem under appropriate hypotheses on functions f and m. By using the Mountain Pass Theorem with Cerami condition, we show the existence of non-trivial weak solution for the problem without assuming the Ambrosetti-Rabinowitz condition. Furthermore, our second purpose is to determine the precise positive interval of λ for which the above problem admits at least two nontrivial weak solutions. It should be noted that the existence of infinitely many weak solutions is proved by employing the Fountain Theorem.