Neumann fractional p-Laplacian: Eigenvalues and existence results. (November 2019)

• Record Type: Journal Article
• Authors: Mugnai, Dimitri; Proietti Lippi, Edoardo
• Is Part Of: Nonlinear analysis. Volume 188(2019)
• Page Start: 455
• Page End: 474
• Publication Date: 2019-11
• Subjects: 35A15 -- 47J30 -- 35S15 -- 47G10 -- 45G05; Fractional p-Laplacian -- Neumann boundary conditions -- Eigenvalues -- Subcritical perturbation; 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.2019.06.015
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We develop some properties of the p -Neumann derivative for the fractional p -Laplacian in bounded domains with general p > 1 . In particular, we prove the existence of a diverging sequence of eigenvalues and we introduce the evolution problem associated to such operators, studying the basic properties of solutions. Finally, we study a nonlinear problem with source in absence of the Ambrosetti–Rabinowitz condition.