On a class of nonvariational problems in fractional Orlicz–Sobolev spaces. (January 2020)

• Record Type: Journal Article
• Authors: Bahrouni, Anouar; Bahrouni, Sabri; Xiang, Mingqi
• Is Part Of: Nonlinear analysis. Volume 190(2020)
• Publication Date: 2020-01
• Subjects: primary 35J60 -- secondary 35J91 35S30 46E35 58E30; Fractional Orlicz–Sobolev space -- Fractional M-Laplacian -- Nonvariational problem -- Pseudomonotone operator; 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.2019.111595
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we deal with a nonlinear problem driven by the fractional M -Laplacian and with a nonlinear nonhomogeneous reaction term. First, we give some further properties for the new fractional Orlicz–Sobolev space. Then, using the theory of nonlinear operators of monotone-type, we show the existence of a nonnegative solution. Our problem is nonvariational in nature.