On a Schro<spacing diaeresis>dinger-Kirchhoff Type Equation Involving the Fractional p-Laplacian without the Ambrosetti-Rabinowitz Condition

In this paper, we consider the existence and multiplicity of many weak solutions for the following fractional Schr odinger-Kirchhoff type equation: (a+b integral integral(2N)(R)|u(x)-u(y)|p/|x-y|(N+ps)dxdy)(p-1)x(-triangle)(s)(p)u+lambda V(x)|u|(p-2)u =f(x,u) +h(x) inR(N), whereN > sp,a,b >0 are constants,lambda is a parameter, (-triangle)spis the frac-tionalp-Laplacian operator with 0< s <1< p <infinity, nonlinearityf(x,u)and potential functionV(x) satisfy some suitable assumptions. Under thoseconditions, some new results are obtained for lambda >0 large enough by applyingthe variation methods