Qualitative Properties of Solutions for an Integral Equation

2003/07/18 by Wenxiong Chen, Congming Li, Chen, Wenxiong +3
Mathematics · #35J99 #45E10 #45G05 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #math.AP #msc:35J99 #msc:45E10 #msc:45G05

paper · pdf · doi:10.48550/arxiv.math/0307262

8 pages

arxiv created 2003/07/18 · openalex publication_date 2003/07/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let n be a positive integer and let 0 < α< n. In this paper, we continue our study of the integral equation u(x) = ∫_Rⁿ \fracu(y)^(n+α)(n-α)|x - y|^n-αdy. We mainly consider singular solutions in subcritical, critical, and super critical cases, and obtain qualitative properties, such as radial symmetry, monotonicity, and upper bounds for the solutions.

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