Existence results for a class of p(x)-Kirchhoff-type equations with critical growth and critical frequency

This article deals with a class of p(x)-Laplace equations with critical growth and critical frequency. By using the variational methods and some analytical skills, we obtain the existence and multiplicity of nontrivial solutions for this problem. The novelty of this paper lies in two aspects: (1) this equation contains the degenerate case, which corresponds to the Kirchhoff term K vanishing at zero and (2) our paper is about the appearance of critical terms, which can be viewed as a partial extension of the results of Zhang et al. [Electron. J. Differ. Equations 2018, 1–20] concerning the existence of solutions to this problem in the subcritical case.