Solvability of a nonlocal fractional p-Kirchhoff type problem

In this work, we solve a Kirchhoff type boundary problem governed by the nonlocal fractional p-Laplacian operator(sic) M (??(R2N) |u(x) - u(y)|K-p(x - y)dxdy) L(K)(p)u = f (x, u), in O, u = 0on R-N\O,where L-K(p) is a non-local operator with singular kernel K, O is an open bounded subset of R-N with smooth boundary ?O, M is a continuous function and the nonlinearity f is a Caratheodory function which does not verify the Ambrosetti-Rabinowitz type condition. Through some adequate assumptions, we prove the existence of nontrivial weak solutions to our problem by applying new skills and variational methods.