Existence and multiplicity of solutions for (p,q)$$ \left(p,q\right) $$‐Laplacian Kirchhoff‐type fractional differential equations with impulses

Abstract

In this paper, we investigate the existence and multiplicity of solutions for a class of ‐Laplacian Kirchhoff‐type impulsive fractional differential equations. First, under a weaker condition than the Ambrosetti–Rabinowitz condition and the Miyagaki–Souto condition, the existence of an unbounded sequence of nontrivial solutions follows from the fountain theorem. Then, some new criteria are given to guarantee that the fractional differential equation has at least two nontrivial solutions using the Nehari manifold method combined with the fibering map.