EXISTENCE AND BIFURCATION OF PERIODIC SOLUTIONS OF THREE-DIMENSIONAL DELAY DIFFERENTIAL EQUATIONS

2004 ◽  
Vol 14 (11) ◽  
pp. 3921-3929 ◽  
Author(s):  
PING BI ◽  
MAOAN HAN
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Delay Differential Equations ◽  
Three Dimensional ◽  
Hopf Bifurcations ◽  
Differential Systems ◽  
Delay Differential Systems ◽  
Delay Differential

In this paper, we develop Kaplan–Yorke's method and consider the existence of 2r/(2k+1)-periodic solutions for certain three-dimensional delay differential systems. We also study Hopf bifurcations of this kind of periodic solutions for the system with a parameter and present some application examples of our main results.

A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3157-3172
Author(s):  
Mujahid Abbas ◽  
Bahru Leyew ◽  
Safeer Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Metric Space ◽  
Delay Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

scholarly journals Global branches of periodic solutions for forced delay differential equations on compact manifolds

2007 ◽  
Vol 233 (2) ◽  
pp. 404-416 ◽  
Author(s):  
Pierluigi Benevieri ◽  
Alessandro Calamai ◽  
Massimo Furi ◽  
Maria Patrizia Pera
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Delay Differential Equations ◽  
Compact Manifolds ◽  
Delay Differential
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