Multiple solutions for a coupled Kirchhoff system with fractional p-Laplacian and sign-changing weight functions. Issue 6 (3rd June 2022)

• Record Type: Journal Article
• Authors: Zhen, Maoding; Yang, Meihua
• Is Part Of: Complex variables and elliptic equations. Volume 67:Issue 6(2022)
• Page Start: 1326
• Page End: 1351
• Publication Date: 2022-06-03
• Subjects: Fractional p-Kirchhoff system -- Nehari manifold -- sign-changing weight functions; 35A15 -- 47G20 -- 35R11; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2020.1870453
• Languages: English
• ISSNs: 1747-6933

Abstract

Abstract : In this paper, we investigate the multiplicity of solutions for Kirchhoff fractional p -Laplacian system in bounded domains: 1 ∑ i = 1 k [ u i ] s, p p θ − 1 ( − Δ ) p s u j ( x ) = λ j f j ( x ) | u j | q − 2 u j + ∑ i ≠ j β i, j h ( x ) | u i | m | u j | m − 2 u j in Ω, u j = 0 i n R n ∖ Ω . By using the Nehari manifold method, together with Ekeland's variational principle, we show that there exist two distinct solutions under suitable conditions on weight functions f j and h . Our results extend and generalize the main results in Xiang et al. [Multiplicity of solutions for a class of quasilinear Kirchhoff system involving the fractional p-Laplacian. Nonlinearity. 2016;29:3186–3205] in Nonlinearity 2016, in which f j, h are constants.