Existence and multiplicity of solutions for a new <i>p</i>(<i>x</i>)-Kirchhoff problem with variable exponents

In this article, we study a class of new p ( x )-Kirchhoff problem without satisfying the Ambrosetti-Rabinowitz type growth condition. Under some suitable superliner conditions, we introduce new methods to show the boundedness of Cerami sequences. By using the mountain pass lemma and the symmetric mountain pass lemma, we prove that the p ( x )-Kirchhoff problem has a nontrivial weak solution and infinitely many solutions.