Positive and Nontrivial Solutions for the Urysohn Integral Equation  

作　　者：Daniel FRANCO Gennaro INFANTE Donal O'REGAN 

机构地区：[1]Departamentode Matemática Aplicada,Universidad Nacional de Educación a Distancia [2]Dipartimentodi Matematica,Universitàdella Calabria [3]Department of Mathematics,National University of Ireland

出　　处：《Acta Mathematica Sinica,English Series》2006年第6期1745-1750,共6页数学学报（英文版）

基　　金：The first and third authors have been supported in part by Ministerio de Cienciay Tecnología(Spain)MTM2004-06652-C03-03

摘　　要：We establish new criteria for the existence of either positive or nonzero solutions of the Urysohn integral equation. We also discuss the existence of an interval of positive eigenvalues and sufficient conditions for the existence of at least a positive eigenvalue with a nonzero or positive eigenfunction for the Urysohn integral operator. Among others, we employ techniques based on fixed point index theory for compact maps, which are new for this type of equation.We establish new criteria for the existence of either positive or nonzero solutions of the Urysohn integral equation. We also discuss the existence of an interval of positive eigenvalues and sufficient conditions for the existence of at least a positive eigenvalue with a nonzero or positive eigenfunction for the Urysohn integral operator. Among others, we employ techniques based on fixed point index theory for compact maps, which are new for this type of equation.

关 键 词：Urysohn integral equation positive solutions EIGENVALUES 

分 类 号：O175.5[理学—数学]