scholarly journals Oscillation Criteria of Solutions of Third Order Neutral Integro-Differential Equations

2021 ◽  
pp. 3642-3647
Author(s):  
Taghreed Hussein Abed ◽  
Sattar Naser Ketab ◽  
Hussain Ali Mohamad
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Third Order ◽  
Oscillation Criteria ◽  
All Solutions ◽  
Necessary And Sufficient

      Some necessary and sufficient conditions are obtained that guarantee the oscillation of all solutions of two types of neutral integro-differential equations of third order. The integral is used in the sense of Riemann-Stieltjes. Some examples were included to illustrate the obtained results

scholarly journals Oscillations of Third Order Half Linear Neutral Differential Equations

2015 ◽  
Vol 12 (3) ◽  
pp. 625-631
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Oscillation Criterion ◽  
Necessary And Sufficient Conditions ◽  
Third Order ◽  
Neutral Differential Equations ◽  
The Third ◽  
All Solutions ◽  
Necessary And Sufficient

In this paper the oscillation criterion was investigated for all solutions of the third-order half linear neutral differential equations. Some necessary and sufficient conditions are established for every solution of (a(t)[(x(t)±p(t)x(?(t) ) )^'' ]^? )^'+q(t) x^? (?(t) )=0, t?t_0, to be oscillatory. Examples are given to illustrate our main results.

scholarly journals On nonoscillatory solutions tending to zero of third-order nonlinear differential equations

2011 ◽  
Vol 48 (1) ◽  
pp. 135-143 ◽  
Author(s):  
Ivan Mojsej ◽  
Alena Tartal’ová
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Third Order ◽  
Nonoscillatory Solutions ◽  
The Third ◽  
Necessary And Sufficient

Abstract The aim of this paper is to present some results concerning with the asymptotic behavior of solutions of nonlinear differential equations of the third-order with quasiderivatives. In particular, we state the necessary and sufficient conditions ensuring the existence of nonoscillatory solutions tending to zero as t → ∞.

12.—Rotation Properties of Adjoint Pairs of Differential Systems

1976 ◽  
Vol 75 (2) ◽  
pp. 149-155
Author(s):  
Kurt Kreith
Keyword(s):  
Differential Equations ◽  
Large Class ◽  
Fourth Order ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Differential Systems ◽  
All Solutions ◽  
Necessary And Sufficient

SYNOPSISA large class of self-adjoint fourth-order differential equations has the property that if one solution is oscillatory then all solutions are oscillatory. This paper establishes necessary and sufficient conditions for this property to hold for a corresponding class of non-self-adjoint differential equations.

scholarly journals Nonoscillation of the solutions of impulsive differential equations of third order

2001 ◽  
Vol 14 (3) ◽  
pp. 309-316 ◽  
Author(s):  
Margarita Boneva Dimitrova
Keyword(s):  
Differential Equations ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Nonoscillatory Solution ◽  
Necessary And Sufficient Conditions ◽  
Third Order ◽  
Impulse Effect ◽  
Necessary And Sufficient

Necessary and sufficient conditions are found for existence of at least one bounded nonoscillatory solution of a class of impulsive differential equations of third order and fixed moments of impulse effect. Some asymptotic properties of the nonoscillating solutions are investigated.

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.

scholarly journals Oscillation Criteria for Third-Order Emden–Fowler Differential Equations with Unbounded Neutral Coefficients

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
George E. Chatzarakis ◽  
Said R. Grace ◽  
Irena Jadlovská ◽  
Tongxing Li ◽  
Ercan Tunç
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Third Order ◽  
Oscillation Criteria ◽  
All Solutions ◽  
New Criteria

New sufficient conditions for the oscillation of all solutions to a class of third-order Emden–Fowler differential equations with unbounded neutral coefficients are established. The criteria obtained essentially improve related results in the literature. In particular, as opposed to known results, new criteria can distinguish solutions of third-order differential equations with different behaviors. Examples are also provided to illustrate the results.

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