Multiple solutions to Kirchhoff-Schrödinger equations involving the $p(\cdot )$-Laplace-type operator

This paper is devoted to deriving several multiplicity results of nontrivial weak solutions to Kirchhoff-Schrödinger equations involving the $p(\cdot )$-Laplace-type operator. The aims of this paper are stated as follows. First, under some conditions on a nonlinear term, we show that our problem has a sequence of infinitely many large energy solutions. Second, we obtain the existence of a sequence of infinitely many small energy solutions to the problem on a new class of nonlinear term. The primary tools to obtain such multiplicity results are the fountain theorem and the dual fountain theorem, respectively.