scholarly journals Oscillation results for second-order neutral differential equations of mixed type

2011 ◽  
Vol 48 (1) ◽  
pp. 101-116 ◽  
Author(s):  
Tongxing Li ◽  
Blanka Baculíková ◽  
Jozef Džurina
Keyword(s):  
Differential Equations ◽  
Mixed Type ◽  
Second Order ◽  
Order Linear ◽  
Neutral Differential Equations ◽  
Equations Of Mixed Type ◽  
Oscillation Theorems

Abstract Some oscillation theorems are established for the second-order linear neutral differential equations of mixed type Several examples are also provided to illustrate the main results.

scholarly journals Oscillation Criteria for Certain Second-Order Nonlinear Neutral Differential Equations of Mixed Type

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Zhenlai Han ◽  
Tongxing Li ◽  
Chenghui Zhang ◽  
Ying Sun
Keyword(s):  
Differential Equations ◽  
Mixed Type ◽  
Second Order ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Equations Of Mixed Type ◽  
Positive Integers

Some oscillation criteria are established for the second-order nonlinear neutral differential equations of mixed type[(x(t)+p1x(t−τ1)+p2x(t+τ2))γ]′​′=q1(t)xγ(t−σ1)+q2(t)xγ(t+σ2),t≥t0, whereγ≥1is a quotient of odd positive integers. Our results generalize the results given in the literature.

scholarly journals An Oscillation Test for Solutions of Second-Order Neutral Differential Equations of Mixed Type

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1634
Author(s):  
Osama Moaaz ◽  
Ali Muhib ◽  
Shyam S. Santra
Keyword(s):  
Differential Equations ◽  
Mixed Type ◽  
Oscillation Theory ◽  
Second Order ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Equations Of Mixed Type ◽  
All Solutions ◽  
Oscillation Test

It is easy to notice the great recent development in the oscillation theory of neutral differential equations. The primary aim of this work is to extend this development to neutral differential equations of mixed type (including both delay and advanced terms). In this work, we consider the second-order non-canonical neutral differential equations of mixed type and establish a new single-condition criterion for the oscillation of all solutions. By using a different approach and many techniques, we obtain improved oscillation criteria that are easy to apply on different models of equations.

scholarly journals Second-Order Non-Canonical Neutral Differential Equations with Mixed Type: Oscillatory Behavior

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 318
Author(s):  
Osama Moaaz ◽  
Amany Nabih ◽  
Hammad Alotaibi ◽  
Y. S. Hamed
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Mixed Type ◽  
Relevant Literature ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Neutral Differential Equations ◽  
Delay Differential ◽  
Oscillation Of Solutions

In this paper, we establish new sufficient conditions for the oscillation of solutions of a class of second-order delay differential equations with a mixed neutral term, which are under the non-canonical condition. The results obtained complement and simplify some known results in the relevant literature. Example illustrating the results is included.

A proof of characterisation of oscillation for higher-order neutral differential equations of mixed type by the Laplace transform

1994 ◽  
Vol 124 (5) ◽  
pp. 909-916 ◽  
Author(s):  
O. Arino ◽  
M. A. El Attar
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
General Expression ◽  
Exponential Growth ◽  
Mixed Type ◽  
Deviating Arguments ◽  
Neutral Differential Equations ◽  
Equations Of Mixed Type ◽  
The Laplace Transform ◽  
Image Position

Consider the general expression of such equations in the formwhere Ai, Bj, ∊ ℝ, δo = 0 dn/ 0, dn are n-derivatives, n ≧ l, the σj'S and δj,'s respectively, are ordered as an increasing family with possibly positive and negative terms. These are the deviating arguments. In this paper, we provide a proof of this result based on the use of the Laplace transform. Our method involves new results regarding the exponential growth of positive solutions for such equations.

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