Properties of eigenvalues and some regularities on fractional p-Laplacian with singular weights. (December 2019)

• Record Type: Journal Article
• Authors: Ho, Ky; Sim, Inbo
• Is Part Of: Nonlinear analysis. Volume 189(2019)
• Publication Date: 2019-12
• Subjects: 35B32 -- 35B45 -- 35B50 -- 35J20 -- 35P15 -- 35P30 -- 35R11; Fractional p-Laplacian -- Bifurcation -- Eigenvalue problem -- A-priori bounds; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111580
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We provide fundamental properties of the first eigenpair for fractional p -Laplacian eigenvalue problems under singular weights, which is related to Hardy type inequality, and also show that the second eigenvalue is well-defined. We obtain a-priori bounds and the continuity of solutions to problems with such singular weights with some additional assumptions. Moreover, applying the above results, we show a global bifurcation emanating from the first eigenvalue, the Fredholm alternative for non-resonant problems, and obtain the existence of infinitely many solutions for some nonlinear problems involving singular weights. These are new results, even for (fractional) Laplacian.