The existence of periodic solutions for nonlinear systems of first-order differential equations at resonance

2000 ◽  
Vol 21 (11) ◽  
pp. 1282-1291 ◽  
Author(s):  
MA Shi-wang ◽  
Wang Zhi-cheng ◽  
Yu Jian-she
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Periodic Solutions ◽  
First Order ◽  
At Resonance ◽  
Existence Of Periodic Solutions ◽  
First Order Differential Equations

scholarly journals ON PERIODIC SOLUTIONS FOR FIRST-ORDER DIFFERENTIAL EQUATIONS INVOLVING THE DISTRIBUTIONAL HENSTOCK–KURZWEIL INTEGRAL

2012 ◽  
Vol 86 (2) ◽  
pp. 327-338 ◽  
Author(s):  
WEI LIU ◽  
GUOJU YE ◽  
YING WANG ◽  
XUEYUAN ZHOU
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Topological Structure ◽  
Solution Set ◽  
First Order ◽  
General Integral ◽  
Existence Of Periodic Solutions ◽  
First Order Differential Equations

AbstractThe purpose of this paper is to study the existence of periodic solutions and the topological structure of the solution set of first-order differential equations involving the distributional Henstock–Kurzweil integral. The distributional Henstock–Kurzweil integral is a general integral, which includes the Lebesgue and Henstock–Kurzweil integrals. The main results extend some previously known results in the literature.

Periodic solutions of ordinary differential equations with one-sided growth restrictions

1978 ◽  
Vol 82 (1-2) ◽  
pp. 95-106 ◽  
Author(s):  
J. Mawhin ◽  
W. Walter
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
First Order ◽  
Asymptotic Nature ◽  
Special Cases ◽  
Existence Of Periodic Solutions ◽  
Growth Restrictions ◽  
Functional Differential ◽  
The Right

SynopsisThe existence of periodic solutions is proved for first order vector ordinary and functional differential equations when the right-hand side satisfies a one-sided growth restriction of Wintner type together with some conditions of asymptotic nature. Special cases in the line of Landesman-Lazer and of Winston are explicited.

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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