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.

scholarly journals New Comparison Theorems for the Nth Order Neutral Differential Equations with Delay Inequalities

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 454 ◽  
Author(s):  
Osama Moaaz ◽  
Shigeru Furuichi ◽  
Ali Muhib
Keyword(s):  
Differential Equations ◽  
Higher Order ◽  
Comparison Theorems ◽  
Differential Inequalities ◽  
Neutral Differential Equations ◽  
First Order ◽  
A New Technique ◽  
Equations With Delay ◽  
Higher Order Differential Equations ◽  
First Order Differential Equations

In this work, we present a new technique for the oscillatory properties of solutions of higher-order differential equations. We set new sufficient criteria for oscillation via comparison with higher-order differential inequalities. Moreover, we use the comparison with first-order differential equations. Finally, we provide an example to illustrate the importance of the results.

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