SOLUTION BRANCHES OF NONLINEAR EIGENVALUE PROBLEMS ON RESTRICTED DOMAINS

被引：0

作者：

ARORA, S. H. A. N. E. ^{[1
]}

机构：

[1] Univ Sydney, Sch Math & Stat, Camperdown, NSW 2006, Australia

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2020年 / 102卷 / 03期

关键词：

nonlinear eigenvalue problem; bifurcation theory; compact operators;

D O I：

10.1017/S0004972720000234

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We extend bifurcation results of nonlinear eigenvalue problems from real Banach spaces to any neighbourhood of a given point. For points of odd multiplicity on these restricted domains, we establish that the component of solutions through the bifurcation point either is unbounded, admits an accumulation point on the boundary, or contains an even number of odd-multiplicity points. In the simple-multiplicity case, we show that branches of solutions in the directions of corresponding eigenvectors satisfy similar conditions on such restricted domains.

引用

页码：490 / 497

页数：8