Year: 2025
Type: article
Abstract: This work establishes the multiplicity of solutions for the fractional Kazdan–Warner equation on finite graphs for the negative case. Our main focus lies in analyzing the nonlinear equation defined on a finite graph (V,E,μ,w): (−Δ)su=(K+λ)e2u−κinV, where the fraction s∈(0,1) and real parameter λ are given, and the graph functions K and κ satisfy maxx∈VK(x)=0, K≢0 and ∫Vκdμ<0. We derive the solvability characteristics of the above equation with the help of variational theory and the upper and lower solutions method.
Source: Axioms
Authors: Liang Shan, Yang Liu
Institution: Renmin University of China
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
OpenAlex ID: W4409965651