Infinitely many solutions for a fractional Kirchhoff type problem via Fountain Theorem. (June 2015) - Xiang, Mingqi; Zhang, Binlin; Guo, Xiuying
Abstract: In this paper, we use the Fountain Theorem and the Dual Fountain Theorem to study the existence of infinitely many solutions for Kirchhoff type equations involving nonlocal integro-differential operators with homogeneous Dirichlet boundary conditions. A model for these operators is given by the fractional Laplacian of Kirchhoff type: M ( ∬ R 2 N | u ( x ) − u ( y ) | 2 | x − y | N + 2 s d x d y ) ( − Δ ) s u ( x ) − λ u = f ( x, u ) in Ω u = 0 in R N ∖ Ω, where Ω is a smooth bounded domain of R N, ( − Δ ) s is the fractional Laplacian operator with 0 < s < 1 and 2 s < N, λ is a real parameter, M is a continuous and positive function and f is a Carathéodory function satisfying the Ambrosetti–Rabinowitz type condition.,