Bounded variation solution to 1-Laplacian Kirchhoff type problem in ℝN. Issue 2 (1st February 2023)

• Record Type: Journal Article
• Authors: Aouaoui, Sami; Dhifet, Mariem
• Is Part Of: Complex variables and elliptic equations. Volume 68:Issue 2(2023)
• Page Start: 200
• Page End: 211
• Publication Date: 2023-02-01
• Subjects: 1-Laplacian -- Kirchhoff type -- nonlocal elliptic equation -- bounded variation functions -- generalized gradient -- variational method; 26A27 -- 26A45 -- 26B25 -- 35D30 -- 35J20 -- 35J62; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2021.1985479
• Languages: English
• ISSNs: 1747-6933

Abstract

Abstract : This paper is concerned with the existence of a nontrivial solution to a class of nonlocal elliptic problems of Kirchhoff type involving the 1-Laplacian operator. This solution will be searched in the space B V ( R N ) of the functions of bounded variation in R N, N ≥ 2 . Because of the irregularity of such kind of space (it is non-reflexive), the proof of our main existence result needs the use of some sophisticated arguments. We highlight the fact that, to the very best knowledge of the authors, this work is the first one dealing with an equation of Kirchhoff type involving the 1-Laplacian.