UNILATERAL BIFURCATION FOR SEVERAL-PARAMETER EIGENVALUE PROBLEM WITH HOMOGENEOUS OPERATOR

doi:10.1007/s10473-019-0517-7

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (5): 1406-1414.doi: 10.1007/s10473-019-0517-7

UNILATERAL BIFURCATION FOR SEVERAL-PARAMETER EIGENVALUE PROBLEM WITH HOMOGENEOUS OPERATOR

曹晓菲¹, 代国伟²

1. Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huaian 223003, China;
2. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

收稿日期:2017-04-17 修回日期:2018-09-17 出版日期:2019-10-25 发布日期:2019-11-11
通讯作者: Xiaofei CAO E-mail:caoxiaofei258@126.com
作者简介:Guowei DAI,E-mail:daiguowei@dlut.edu.cn
基金资助:
The second author was supported by National Natural Science Foundation of China (11871129).

UNILATERAL BIFURCATION FOR SEVERAL-PARAMETER EIGENVALUE PROBLEM WITH HOMOGENEOUS OPERATOR

Xiaofei CAO¹, Guowei DAI²

1. Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huaian 223003, China;
2. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

Received:2017-04-17 Revised:2018-09-17 Online:2019-10-25 Published:2019-11-11
Contact: Xiaofei CAO E-mail:caoxiaofei258@126.com
Supported by:
The second author was supported by National Natural Science Foundation of China (11871129).

摘要/Abstract

摘要： We establish the unilateral global bifurcation result for the following nonlinear operator equation
u=L(λ)u + H(λ, u), (λ, u) ∈ R^m×X
where m is a positive integer, X is a Banach space, L(·) is a positively homogeneous completely continuous operator and H:R^m×X → X is completely continuous with H=o (||u||) near u=0 uniformly on bounded λ sets.

关键词: global bifurcation, several-parameter, nonlinear problem

Abstract: We establish the unilateral global bifurcation result for the following nonlinear operator equation
u=L(λ)u + H(λ, u), (λ, u) ∈ R^m×X
where m is a positive integer, X is a Banach space, L(·) is a positively homogeneous completely continuous operator and H:R^m×X → X is completely continuous with H=o (||u||) near u=0 uniformly on bounded λ sets.

Key words: global bifurcation, several-parameter, nonlinear problem

中图分类号:

47J15

曹晓菲, 代国伟. UNILATERAL BIFURCATION FOR SEVERAL-PARAMETER EIGENVALUE PROBLEM WITH HOMOGENEOUS OPERATOR[J]. 数学物理学报(英文版), 2019, 39(5): 1406-1414.

Xiaofei CAO, Guowei DAI. UNILATERAL BIFURCATION FOR SEVERAL-PARAMETER EIGENVALUE PROBLEM WITH HOMOGENEOUS OPERATOR[J]. Acta mathematica scientia,Series B, 2019, 39(5): 1406-1414.

UNILATERAL BIFURCATION FOR SEVERAL-PARAMETER EIGENVALUE PROBLEM WITH HOMOGENEOUS OPERATOR

UNILATERAL BIFURCATION FOR SEVERAL-PARAMETER EIGENVALUE PROBLEM WITH HOMOGENEOUS OPERATOR

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