Solutions of Fully Nonlinear Nonlocal Systems

2016/08/30 by Pengyan Wang, Mei Yu, Wang, Pengyan +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1608.08371

openalex publication_date 2016/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider the system involving fully nonlinear nonlocal operators: \ F_α(u(x)) = C_n,α PV ∫_Rⁿ \fracG(u(x)-u(y))|x-y|^n+α dy=f(v(x)), F_β(v(x)) = C_n,β PV ∫_Rⁿ \fracG(v(x)-v(y))|x-y|^n+β dy=g(u(x)). . A narrow region principle and a decay at infinity for the system for carrying on the method of moving planes are established. Then we prove the radial symmetry and monotonicity for positive solutions to the nonlinear system in the whole space. Non-existence of positive solutions to the nonlinear system on a half space is proved.

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