A critical Kirchhoff type problem involving the fractional Laplacian in. Issue 5 (4th May 2018) - Xiang, Mingqi; Zhang, Binlin; Zhang, Xia
Abstract: In this paper, we are concerned with the existence of solutions for a critical p -Kirchhoff type problem driven by a nonlocal integro-differential operator: where is a continuous function, is a singular kernel function, is a nonlocal fractional operator, with, , f is a Carathéodory function on satisfying the Ambrosetti–Rabinowitz type condition. Under some suitable assumptions, we obtain the existence of nontrivial solutions for above problem by applying the mountain pass theorem. A distinguished feature of this paper is that M (0) may be zero, which means that the problem is degenerate. Consequently, the main theorem extends in several directions the recent results of Autuori, Fiscella and Pucci [Nonlinear Anal. 2015;125:699–714].