Eigenvalue problems and fixed point theorems for a class of positive nonlinear operators

被引：3

作者：

Huang, Min-Jei ^{[1
]}

Huang, Chao-Ya

Tsai, Tzong-Mo

机构：

[1] Natl Tsing Hua Univ, Dept Math, Hsinchu 30043, Taiwan

[2] Mingchi Univ Technol, Dept Elect Engn, Atsugi, Kanagawa 24301, Japan

来源：

MATHEMATISCHE ZEITSCHRIFT | 2007年 / 257卷 / 03期

关键词：

eigenvalue problem; fixed point; cone; projective metric; concave operator; compact operator;

D O I：

10.1007/s00209-007-0136-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the eigenvalue problems for a class of positive nonlinear operators defined on a cone in a Banach space. Using projective metric techniques and Schauder's fixed-point theorem, we establish existence, uniqueness, monotonicity and continuity results for the eigensolutions. Moreover, the method leads to a result on the existence of a unique fixed point of the operator. Applications to nonlinear boundary-value problems, to differential delay equations and to matrix equations are considered.

引用

页码：581 / 595

页数：15

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