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

Abstract

The aim of this paper was to investigate the existence of radial solutions for a Kirchhoff-type problem driven by the fractional Laplacian, that iswhere is the fractional Laplacian operator with and , and are constants, is a parameter and without the Ambrosetti–Rabinowitz condition. The existence of nontrivial nonnegative radial solutions is obtained using variational methods combined with a cut-off function technique.