A critical Kirchhoff type problem involving the fractional Laplacian in. Issue 5 (4th May 2018)

• Record Type: Journal Article
• Authors: Xiang, Mingqi; Zhang, Binlin; Zhang, Xia
• Is Part Of: Complex variables and elliptic equations. Volume 63:Issue 5(2018)
• Page Start: 652
• Page End: 670
• Publication Date: 2018-05-04
• Subjects: Integro-differential operators -- fractional p–Kirhhoff equations -- critical exponent -- mountain pass theorem; 35D30 -- 35R11 -- 35A15 -- 47G20; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2017.1332050
• Languages: English
• ISSNs: 1747-6933

Abstract

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].