The necessary and sufficient conditions for the existence of periodic solutions of a type of neutral functional differential equations

1991 ◽  
Vol 7 (1) ◽  
pp. 74-79
Author(s):  
Yi Zhang ◽  
Yi Zhang
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Neutral Functional Differential Equations ◽  
Existence Of Periodic Solutions ◽  
Functional Differential ◽  
Necessary And Sufficient

scholarly journals Asymptotically power solutions of higher order neutral functional differential equations

2004 ◽  
Vol 35 (4) ◽  
pp. 383-389
Author(s):  
Zhi-Qiang Zhu ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Necessary And Sufficient Conditions ◽  
Neutral Functional Differential Equations ◽  
Polynomial Solutions ◽  
Functional Differential ◽  
Necessary And Sufficient

Necessary and sufficient conditions are derived for the existence of asymptotically polynomial solutions of a class of neutral functional differential equations.

PERIODIC SOLUTIONS OF FORCED OSCILLATORS WITH SEVERAL DEGREES OF FREEDOM

2002 ◽  
Vol 34 (3) ◽  
pp. 308-318 ◽  
Author(s):  
RAFAEL ORTEGA ◽  
LUIS A. SÁNCHEZ
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Degrees Of Freedom ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Forced Oscillators ◽  
Existence Of Periodic Solutions ◽  
Necessary And Sufficient ◽  
New Phenomena

Results of the Landesman–Lazer type provide necessary and sufficient conditions for the existence of periodic solutions of certain nonlinear differential equations with forcing. Typically, they deal with scalar problems. This paper presents a discussion of possible extensions to systems. The emphasis is placed on the new phenomena produced by the increase of the dimension.

scholarly journals A Note on the Periodic Solutions for a Class of Third Order Differential Equations

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 31
Author(s):  
Zouhair Diab ◽  
Juan L. G. Guirao ◽  
Juan A. Vera
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Monodromy Matrix ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Averaging Theory ◽  
Third Order ◽  
Existence Of Periodic Solutions ◽  
The Stability ◽  
Necessary And Sufficient

The aim of the present work is to study the necessary and sufficient conditions for the existence of periodic solutions for a class of third order differential equations by using the averaging theory. Moreover, we use the symmetry of the Monodromy matrix to study the stability of these solutions.

Existence of positive periodic solutions for a class of second-order neutral functional differential equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
He Yang ◽  
Lu Zhang
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Fixed Point Index ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Index Theory ◽  
Second Order ◽  
Neutral Functional Differential Equations ◽  
Fixed Point Index Theory ◽  
Functional Differential

Abstract In this paper, under some ordered conditions, we investigate the existence of positive ω-periodic solutions for a class of second-order neutral functional differential equations with delayed derivative in nonlinearity of the form (x(t) − cx(t − δ))″ + a(t)g(x(t))x(t) = λb(t)f(t, x(t), x(t − τ 1(t)), x′(t − τ 2(t))). By utilizing the perturbation method of a positive operator and the fixed point index theory in cones, some sufficient conditions are established for the existence as well as the non-existence of positive ω-periodic solutions.

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