NONLINEAR PERRON-FROBENIUS PROBLEM FOR ORDER-PRESERVING MAPPINGS .1.

被引：3
|
作者：
OGIWARA, T [1 ]
机构：
[1] UNIV TOKYO, DEPT MATH SCI, TOKYO 113, JAPAN
来源：
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES | 1993年 / 69卷 / 08期
关键词：
PERRON-FROBENIUS; ORDER-PRESERVING; INDECOMPOSABLE; MAXIMAL EIGENVALUE; POSITIVE EIGENVECTOR;
D O I：
10.3792/pjaa.69.312
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the eigenvalue problem of an order-preserving mapping defined on a positive cone of an ordered Banach space. Among other things, we prove the existence and, in some cases, the uniqueness of the positive eigenvalue. We also discuss other properties of eigenvalues and eigenvectors. The notion of indecomposability for nonlinear mappings that we introduce in an infinite dimensional setting will play a key role in our argument. We apply the results in this paper to boundary value problems for a class of partial differential equations in part II.
引用
收藏
页码：312 / 316
页数：5
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