Existence of positive periodic solutions of first-order neutral differential equations

2016 ◽  
Vol 40 (1) ◽  
pp. 205-209 ◽  
Author(s):  
Tuncay Candan
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Positive Periodic Solutions ◽  
Neutral Differential Equations ◽  
First Order

scholarly journals The Existence and Application of Unbounded Connected Components

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Hua Luo ◽  
Ruyun Ma
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Connected Components ◽  
Global Behavior ◽  
Positive Periodic Solutions ◽  
First Order ◽  
Physiological Processes ◽  
Equations With Delay ◽  
First Order Differential Equations

LetXbe a Banach space andCna family of connected subsets ofR×X. We prove the existence of unbounded components in superior limit of{Cn}, denoted bylim¯ Cn, which have prescribed shapes. As applications, we investigate the global behavior of the set of positive periodic solutions to nonlinear first-order differential equations with delay, which can be used for modeling physiological processes.

scholarly journals Positive solutions of differential equations with unbounded Green’s kernel

2012 ◽  
Vol 6 (2) ◽  
pp. 159-173
Author(s):  
John Graef ◽  
Seshadev Padhi ◽  
Smita Pati ◽  
P.K. Kar
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Positive Solutions ◽  
Ecological Model ◽  
Sufficient Conditions ◽  
Allee Effects ◽  
Positive Periodic Solutions ◽  
First Order ◽  
First Order Differential Equations

Sufficient conditions are obtained for the existence/nonexistence of at least two positive periodic solutions of a class of first order differential equations having an unbounded Green?s function. An application to an ecological model with strong Allee effects is also given.

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