Newtonian potential and positive solutions of Poisson equations. (July 2020)

• Record Type: Journal Article
• Authors: Yang, Guangchong; Lan, Kunquan
• Is Part Of: Nonlinear analysis. Volume 196(2020)
• Publication Date: 2020-07
• Subjects: primary 35J05 -- secondary 47G40 47H10 92B05; Newtonian potential operator -- Poisson's equations -- Connectedness -- Smoothness -- Positive solution -- Fixed point theorem -- Population models; 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.2020.111811
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the properties of the well-known Newtonian potential operator including its domain, codomain, compactness, relation with the Poisson's equation and the spectral radii of the weight Newtonian potential operators. These new properties are then applied to study the existence of positive classical solutions of nonlinear Poisson's equations in bounded open sets, which are required neither to be connected nor smooth on their boundaries. The connectedness and smoothness are common requirements for studying the existence of classical or weak solutions of linear or nonlinear elliptic boundary value problems in the literature. Some applications to population models are provided.