Global bifurcation on time scales

被引：25

作者：

Davidson, FA ^{[1
]}

Rynne, BP

机构：

[1] Univ Dundee, Dept Math, Dundee DD1 4HN, Scotland

[2] Heriot Watt Univ, Dept Math, Edinburgh EH14 4AS, Midlothian, Scotland

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2002年 / 267卷 / 01期

关键词：

Sturm-Liouville; time scale; global bifurcation;

D O I：

10.1006/jmaa.2001.7780

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the structure of the solution set of a nonlinear Sturm-Liouville boundary value problem defined on a general time scale. Using global bifurcation theory we show that unbounded continua of nontrivial solutions bifurcate from the trivial solution at the eigenvalues of the linearization, and we show that certain nodal properties of the solutions are preserved along these continua. These results extend the well-known results of Rabinowitz for the case of Sturm-Liouville ordinary differential equations. (C) 2002 Elsevier Science (USA).

引用

页码：345 / 360

页数：16

共 50 条

[21] GLOBAL BIFURCATION OF SOLUTIONS FOR CRIME MODELING EQUATIONS
Cantrell, Robert Stephen
Cosner, Chris
Manasevich, Raul
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2012, 44 (03) : 1340 - 1358
[22] Global Exponential Stability of Impulsive Delayed Neural Networks on Time Scales Based on Convex Combination Method
Wan, Peng
Zeng, Zhigang
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS, 2022, 52 (05): : 3015 - 3024
[23] Existence and global exponential stability of equilibrium of competitive neural networks with different time scales and multiple delays
Gu, Haibo
Jiang, Haijun
Teng, Zhidong
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2010, 347 (05): : 719 - 731
[24] LAGRANGE INTERPOLATION ON TIME SCALES
Georgiev, Svetlin G.
Erhan, Inci M.
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2022, 12 (04): : 1294 - 1307
[25] Gronwall inequalities on time scales
Wong, FH
Yeh, CC
Hong, CH
MATHEMATICAL INEQUALITIES & APPLICATIONS, 2006, 9 (01): : 75 - 86
[26] Analysis of GNSS Time Scales
Bogdanov, Petr
Druzhin, Andrei
Primakina, Tatiana
Tiuliakov, Arkadii
2018 EUROPEAN FREQUENCY AND TIME FORUM (EFTF), 2018, : 181 - 184
[27] αβ-STATISTICAL CONVERGENCE ON TIME SCALES
Sozbir, Bayram
Altundag, Selma
FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS, 2020, 35 (01): : 141 - 150
[28] Eventual disconjugacy on time scales
Davis, JM
Prasad, KR
APPLIED MATHEMATICS LETTERS, 2000, 13 (06) : 77 - 82
[29] Multiple global bifurcation branches for nonlinear Picard problems
Gulgowski, Jacek
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2009, (33) : 1 - 15
[30] Global bifurcation result for the p-biharmonic operator
Drabek, Pavel
Otani, Mitsuharu
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2001,

← 1 2 3 4 5 →