scholarly journals Oscillation conditions in scalar linear delay differential equations

1986 ◽  
Vol 34 (1) ◽  
pp. 1-9 ◽  
Author(s):  
István Győri
Keyword(s):  
Differential Equation ◽  
Delay Differential Equations ◽  
Linear Functional ◽  
Sufficient Conditions ◽  
All Solutions ◽  
Linear Delay ◽  
General Scalar ◽  
Linear Functional Differential Equation ◽  
Functional Differential ◽  
Delay Differential

Sufficient conditions are obtained for all solutions of a general scalar linear functional differential equation to be oscillatory. Our main theorem concerns some particular cases of a conjecture of Hunt and Yorke.

scholarly journals Necessary and Sufficient Conditions for Oscillation of Second-Order Delay Differential Equations

2020 ◽  
Vol 75 (1) ◽  
pp. 135-146
Author(s):  
Shyam Sundar Santra
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Necessary And Sufficient Conditions ◽  
All Solutions ◽  
Linear Delay ◽  
Delay Differential ◽  
Necessary And Sufficient

AbstractIn this work, we obtain necessary and sufficient conditions for the oscillation of all solutions of second-order half-linear delay differential equation of the form {\left( {r{{\left( {x'} \right)}^\gamma }} \right)^\prime }\left( t \right) + q\left( t \right){x^\alpha }\left( {\tau \left( t \right)} \right) = 0Under the assumption ∫∞(r(n))−1/γdη=∞, we consider the two cases when γ > α and γ < α. Further, some illustrative examples showing applicability of the new results are included, and state an open problem.

scholarly journals Oscillation of Fourth-Order Functional Differential Equations with Distributed Delay

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 61 ◽  
Author(s):  
Clemente Cesarano ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
All Solutions ◽  
Functional Differential ◽  
Delay Differential ◽  
Comparison Technique

In this paper, the authors obtain some new sufficient conditions for the oscillation of all solutions of the fourth order delay differential equations. Some new oscillatory criteria are obtained by using the generalized Riccati transformations and comparison technique with first order delay differential equation. Our results extend and improve many well-known results for oscillation of solutions to a class of fourth-order delay differential equations. The effectiveness of the obtained criteria is illustrated via examples.

scholarly journals A Natural Homotopy Analysis Method for Nonlinear Delay Differential Equations

2019 ◽  
Vol 1 (2) ◽  
pp. 86-90
Author(s):  
Aminu Barde
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Delay Differential Equations ◽  
Analysis Method ◽  
Linear Delay ◽  
Homotopy Analysis ◽  
Nonlinear Delay Differential Equations ◽  
Functional Differential ◽  
Delay Differential

Delay differential equation (DDEs) is a type of functional differential equation arising in numerous applications from different areas of studies, for example biology, engineering population dynamics, medicine, physics, control theory, and many others. However, determining the solution of delay differential equations has become a difficult task more especially the nonlinear type. Therefore, this work proposes a new analytical method for solving non-linear delay differential equations. The new method is combination of Natural transform and Homotopy analysis method. The approach gives solutions inform of rapid convergence series where the nonlinear terms are simply computed using He's polynomial. Some examples are given, and the results obtained indicate that the approach is efficient in solving different form of nonlinear DDEs which reduces the computational sizes and avoid round-off of errors.

scholarly journals Oscillations of First Order Linear Delay Differential Equations with positive and negative coefficients

2011 ◽  
Vol 8 (3) ◽  
pp. 806-809
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Oscillation Criteria ◽  
Order Linear ◽  
First Order ◽  
Positive And Negative Coefficients ◽  
All Solutions ◽  
Linear Delay ◽  
Delay Differential

Oscillation criteria are obtained for all solutions of the first-order linear delay differential equations with positive and negative coefficients where we established some sufficient conditions so that every solution of (1.1) oscillate. This paper generalized the results in [11]. Some examples are considered to illustrate our main results.

Oscillation in Differential Equations with Positive and Negative Coefficients

1990 ◽  
Vol 33 (4) ◽  
pp. 442-451 ◽  
Author(s):  
G. Ladas ◽  
C. Qian
Keyword(s):  
Differential Equation ◽  
Asymptotic Stability ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Neutral Differential Equations ◽  
Positive And Negative Coefficients ◽  
All Solutions ◽  
Linear Delay ◽  
Image Position ◽  
Delay Differential

AbstractWe obtain sufficient conditions for the oscillation of all solutions of the linear delay differential equation with positive and negative coefficientswhereExtensions to neutral differential equations and some applications to the global asymptotic stability of the trivial solution are also given.

scholarly journals Second-Order Differential Equation: Oscillation Theorems and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Shyam S. Santra ◽  
Omar Bazighifan ◽  
Hijaz Ahmad ◽  
Yu-Ming Chu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Delay ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Oscillation Theorems

Differential equations of second order appear in a wide variety of applications in physics, mathematics, and engineering. In this paper, necessary and sufficient conditions are established for oscillations of solutions to second-order half-linear delay differential equations of the form ς y u ′ y a ′ + p y u c ϑ y = 0 ,  for  y ≥ y 0 , under the assumption ∫ ∞ ς η − 1 / a = ∞ . Two cases are considered for a < c and a > c , where a and c are the quotients of two positive odd integers. Two examples are given to show the effectiveness and applicability of the result.

scholarly journals On the oscillation of first-order neutral delay differential equations with real coefficients

2002 ◽  
Vol 29 (4) ◽  
pp. 245-249 ◽  
Author(s):  
Ibrahim R. Al-Amri
Keyword(s):  
Differential Equation ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Neutral Delay ◽  
First Order ◽  
Neutral Delay Differential Equation ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
T Tau

We prove sufficient conditions for the oscillation of all solutions of a scalar first-order neutral delay differential equationx˙(t)−cx˙(t−τ)+∑i=1npix(t−σi)=0for all0<c<1,τ,σi>0, andpi∈ℝ,i=1,2,…,n.

Stability analysis of uncertain delay differential equations

2021 ◽  
pp. 1-11
Author(s):  
Jian Wang ◽  
Yuanguo Zhu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Liu Process ◽  
Uncertain Dynamical System ◽  
Analytic Expression ◽  
Functional Differential ◽  
The One ◽  
Delay Differential

Uncertain delay differential equation is a class of functional differential equations driven by Liu process. It is an important model to describe the evolution process of uncertain dynamical system. In this paper, on the one hand, the analytic expression of a class of linear uncertain delay differential equations are investigated. On the other hand, the new sufficient conditions for uncertain delay differential equations being stable in measure and in mean are presented by using retarded-type Gronwall inequality. Several examples show that our stability conditions are superior to the existing results.

scholarly journals Sufficient and necessary conditions for oscillation of linear fractional-order delay differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Qiong Meng ◽  
Zhen Jin ◽  
Guirong Liu
Keyword(s):  
Differential Equation ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Multiple Delays ◽  
All Solutions ◽  
Sufficient And Necessary Conditions ◽  
Delay Differential ◽  
T Tau ◽  
Sufficient And Necessary Condition

AbstractThis paper studies the linear fractional-order delay differential equation $$ {}^{C}D^{\alpha }_{-}x(t)-px(t-\tau )= 0, $$ D − α C x ( t ) − p x ( t − τ ) = 0 , where $0<\alpha =\frac{\text{odd integer}}{\text{odd integer}}<1$ 0 < α = odd integer odd integer < 1 , $p, \tau >0$ p , τ > 0 , ${}^{C}D_{-}^{\alpha }x(t)=-\Gamma ^{-1}(1-\alpha )\int _{t}^{\infty }(s-t)^{- \alpha }x'(s)\,ds$ D − α C x ( t ) = − Γ − 1 ( 1 − α ) ∫ t ∞ ( s − t ) − α x ′ ( s ) d s . We obtain the conclusion that $$ p^{1/\alpha } \tau >\alpha /e $$ p 1 / α τ > α / e is a sufficient and necessary condition of the oscillations for all solutions of Eq. (*). At the same time, some sufficient conditions are obtained for the oscillations of multiple delays linear fractional differential equation. Several examples are given to illustrate our theorems.

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