Multiplicity of weak solutions to non-local elliptic equations involving the fractional p(x)-Laplacian

This paper is devoted to study the several existence results of a sequence of infinitely many solutions to the nonlocal elliptic problem involving the fractional p(x)-Laplacian without assuming the Ambrosetti and Rabinowitz type condition. The strategy of the proof for these results is to approach the problem variationally by using the fountain theorem and the dual fountain theorem. In addition, we prove that the sequence of weak solutions becomes bounded solutions.