Multiple solutions for a singular fractional Kirchhoff problem

In this manuscript, we employed some variational techniques to investigate the existence and the multiplicity of solutions for a fractional equation of Kirchhoff type governed by a non-local elliptic integro-differential operator. More precisely, we use the Mountain pass theorem to establish the existence of a solution for such a problem. Moreover, we use the symmetric version of the mountain pass theorem for even functional, to demonstrate the existence of infinitely many solutions. An example is presented at the end of this work to illustrate our main results.