A fractional Kirchhoff-type problem in RN without the (AR) condition

The aim of this paper was to investigate the existence of radial solutions for a Kirchhoff-type problem driven by the fractional Laplacian, that is [a + b(integral(RN) vertical bar(- Delta)(s/2) u(x)vertical bar(2)dx + integral(RN) vertical bar u vertical bar(2)dx)(theta-1)] x [(- Delta)(s) u + u] = f (u) in R-N, where (- Delta)(s) is the fractional Laplacian operator with 0 < s < 1 and 2s < N, theta > 1 and a > 0 are constants, b >= 0 is a parameter and f is an element of C(R, R) without the Ambrosetti-Rabinowitz condition. The existence of nontrivial nonnegative radial solutions is obtained using variational methods combined with a cut-off function technique.