scholarly journals Existence of Nonoscillatory Solutions of First-Order Neutral Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Božena Dorociaková ◽  
Anna Najmanová ◽  
Rudolf Olach
Keyword(s):  
Differential Equations ◽  
Positive Solutions ◽  
Sufficient Conditions ◽  
Nonoscillatory Solutions ◽  
Neutral Differential Equations ◽  
First Order ◽  
Existence Of Positive Solutions ◽  
Positive Functions ◽  
Bounded Below

This paper contains some sufficient conditions for the existence of positive solutions which are bounded below and above by positive functions for the first-order nonlinear neutral differential equations. These equations can also support the existence of positive solutions approaching zero at infinity

scholarly journals Existence of Positive Solutions of Neutral Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
B. Dorociaková ◽  
M. Kubjatková ◽  
R. Olach
Keyword(s):  
Differential Equations ◽  
Positive Solutions ◽  
Higher Order ◽  
Neutral Differential Equations ◽  
Existence Of Positive Solutions ◽  
Positive Functions ◽  
Bounded Below

The paper contains some suffcient conditions for the existence of positive solutions which are bounded below and above by positive functions for the nonlinear neutral differential equations of higher order. These equations can also support the existence of positive solutions approaching zero at infinity.

scholarly journals First Order Nonlinear Neutral Delay Differential Equations

2004 ◽  
Vol 1 (2) ◽  
pp. 347-349 ◽  
Author(s):  
Baghdad Science Journal
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Neutral Delay ◽  
Nonoscillatory Solutions ◽  
Neutral Differential Equations ◽  
First Order ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

The author obtain results on the asymptotic behavior of the nonoscillatory solutions of first order nonlinear neutral differential equations. Keywords. Neutral differential equations, Oscillatory and Nonoscillatory solutions.

scholarly journals On Nonoscillation of Advanced Differential Equations with Several Terms

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
L. Berezansky ◽  
E. Braverman
Keyword(s):  
Differential Equations ◽  
Positive Solutions ◽  
Nonoscillatory Solutions ◽  
Positive And Negative Coefficients ◽  
Existence Of Positive Solutions

Existence of positive solutions for advanced equations with several termsx˙(t)+∑k=1mak(t)x(hk(t))=0,  hk(t)≥tis investigated in the following three cases: (a) all coefficientsakare positive; (b) all coefficientsakare negative; (c) there is an equal number of positive and negative coefficients. Results on asymptotics of nonoscillatory solutions are also presented.

scholarly journals New criteria for oscillation of nonlinear neutral differential equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Osama Moaaz
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Delay Equations ◽  
Neutral Differential Equation ◽  
Neutral Differential Equations ◽  
First Order ◽  
Riccati Substitution ◽  
Gamma S ◽  
New Criteria

AbstractThe aim of this work is to offer sufficient conditions for the oscillation of neutral differential equation second order $$ \bigl( r ( t ) \bigl[ \bigl( y ( t ) +p ( t ) y \bigl( \tau ( t ) \bigr) \bigr) ^{\prime } \bigr] ^{\gamma } \bigr) ^{\prime }+f \bigl( t,y \bigl( \sigma ( t ) \bigr) \bigr) =0, $$(r(t)[(y(t)+p(t)y(τ(t)))′]γ)′+f(t,y(σ(t)))=0, where $\int ^{\infty }r^{-1/\gamma } ( s ) \,\mathrm{d}s= \infty $∫∞r−1/γ(s)ds=∞. Based on the comparison with first order delay equations and by employ the Riccati substitution technique, we improve and complement a number of well-known results. Some examples are provided to show the importance of these results.

scholarly journals Existence of nonoscillatory solutions of higher order neutral differential equations

Filomat ◽  
2016 ◽  
Vol 30 (8) ◽  
pp. 2147-2153 ◽  
Author(s):  
T. Candan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Nonoscillatory Solutions ◽  
Deviating Arguments ◽  
Neutral Differential Equations ◽  
Distributed Deviating Arguments

This article is concerned with nonoscillatory solutions of higher order nonlinear neutral differential equations with deviating and distributed deviating arguments. By using Knaster-Tarski fixed point theorem, new sufficient conditions are established. Illustrative example is given to show applicability of results.

Oscillation and Nonoscillation Properties of Neutral Differential Equations

1994 ◽  
Vol 46 (2) ◽  
pp. 284-297 ◽  
Author(s):  
L. H. Erbe ◽  
Qingkai Kong
Keyword(s):  
Differential Equations ◽  
Delay Equation ◽  
Neutral Delay ◽  
Nonoscillatory Solutions ◽  
Neutral Differential Equations ◽  
First Order ◽  
Comparison Results ◽  
Oscillation And Nonoscillation

AbstractWe obtain a number of new conditions for oscillation of the first order neutral delay equation with nonconstant coefficients of the formComparison results are also given as well as conditions for the existence of nonoscillatory solutions.

Existence of nonoscillatory solutions of higher order neutral differential equations with distributed deviating arguments

2013 ◽  
Vol 63 (1) ◽  
Author(s):  
T. Candan ◽  
R. Dahiya
Keyword(s):  
Differential Equations ◽  
Variable Coefficient ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Nonoscillatory Solutions ◽  
Deviating Arguments ◽  
Neutral Differential Equations ◽  
Distributed Deviating Arguments ◽  
Banach Contraction ◽  
The Banach Contraction Principle

AbstractIn this work, we consider the existence of nonoscillatory solutions of variable coefficient higher order linear neutral differential equations with distributed deviating arguments. We use the Banach contraction principle to obtain new sufficient conditions, which are weaker than those known, for the existence of nonoscillatory solutions.

scholarly journals Property of oscillation of first order impulsive neutral differential equations with positive and negative coefficients

2019 ◽  
Vol 11 (1) ◽  
Author(s):  
Hussain Ali Mohamad ◽  
Aqeel Falih Jaddoa
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Variable Coefficients ◽  
Neutral Differential Equations ◽  
First Order ◽  
Positive And Negative Coefficients ◽  
Variable Delays ◽  
Impulsive Neutral Differential Equations ◽  
Necessary And Sufficient

            In this paper, necessary and sufficient conditions for oscillation are obtained, so that every solution of the linear impulsive neutral differential equation with variable delays and variable coefficients oscillates. Most of authors who study the oscillatory criteria of impulsive neutral differential equations, investigate the case of constant delays and variable coefficients. However the points of impulsive in this paper are more general. An illustrate example is given to demonstrate our claim and explain the results.

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