Oscillation results for higher order nonlinear neutral differential equations with positive and negative coefficients

2015 ◽  
Vol 21 (2) ◽  
Author(s):  
Saroj Panigrahi ◽  
Rakhee Basu
Keyword(s):  
Fixed Point ◽  
Asymptotic Behavior ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Asymptotic Behavior Of Solutions ◽  
Banach Fixed Point Theorem ◽  
Neutral Differential Equations ◽  
Positive And Negative Coefficients

AbstractIn this paper, the authors investigated oscillatory and asymptotic behavior of solutions of a class of nonlinear higher order neutral differential equations with positive and negative coefficients. The results in this paper generalize the results of Tripathy, Panigrahi and Basu [Fasc. Math. 52 (2014), 155–174]. We establish new conditions which guarantees that every solution either oscillatory or converges to zero. Moreover, using the Banach Fixed Point Theorem sufficient conditions are obtained for the existence of bounded positive solutions. Examples are considered to illustrate the main 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.

scholarly journals New Sufficient Conditions to Ulam Stabilities for a Class of Higher Order Integro-Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2068
Author(s):  
Alberto M. Simões ◽  
Fernando Carapau ◽  
Paulo Correia
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Banach Fixed Point Theorem ◽  
Ulam Stability ◽  
Different Types

In this work, we present sufficient conditions in order to establish different types of Ulam stabilities for a class of higher order integro-differential equations. In particular, we consider a new kind of stability, the σ-semi-Hyers-Ulam stability, which is in some sense between the Hyers–Ulam and the Hyers–Ulam–Rassias stabilities. These new sufficient conditions result from the application of the Banach Fixed Point Theorem, and by applying a specific generalization of the Bielecki metric.

scholarly journals Existence of Nonoscillation Solutions of Second-order Neutral Dierential Equations

2020 ◽  
pp. 1-7
Author(s):  
Zhao Yu-Ping ◽  
Fu Hua
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Second Order ◽  
Neutral Differential Equations ◽  
Positive And Negative Coefficients ◽  
Special Case

This paper is concerned with existence of nonoscillation solution for a family of second-order neutral differential equations with positive and negative coefficients. A sufficient conditions for existence of nonoscillation solution is obtained by contraction fixed point theorem, special case of the equation has also been studied.

scholarly journals Uniqueness and Stability Results on Non-local Stochastic Random Impulsive Integro-Differential Equations

2021 ◽  
Vol 2 (3) ◽  
pp. 9-20
Author(s):  
VARSHINI S ◽  
BANUPRIYA K ◽  
RAMKUMAR K ◽  
RAVIKUMAR K
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Local Conditions ◽  
Non Local ◽  
Inequality Techniques ◽  
Stability Results

The paper is concerned with stochastic random impulsive integro-differential equations with non-local conditions. The sufficient conditions guarantees uniqueness of mild solution derived using Banach fixed point theorem. Stability of the solution is derived by incorporating Banach fixed point theorem with certain inequality techniques.

scholarly journals EXISTENCE OF NONOSCILLATORY RELATIVELY BOUNDED SOLUTIONS OF SECOND ORDER NEUTRAL DIFFERENTIAL EQUATIONS

2019 ◽  
Vol 11 (2) ◽  
pp. 63-71
Author(s):  
Bashar Ahmed Jawad Sharba ◽  
Hussain Ali Mohamad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Convergence Theorem ◽  
Sufficient Conditions ◽  
Bounded Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Neutral Differential Equations ◽  
Existence Of Positive Solutions ◽  
Dominated Convergence

In this paper some sufficient conditions are obtained to insure the existence of positive solutions which is relatively bounded from one side for nonlinear neutral differential equations of second order.Weused the Krasnoselskii’s fixed point theorem and Lebesgue’s dominated convergence theorem to obtain new sufficient conditions for the existence of a Nonoscillatoryone side relatively boundedsolutions.These conditions are more applicable than some known results in the references. Three examples included to illustrate the results obtained.

Oscillation results for third order nonlinear mixed neutral differential equations

2016 ◽  
Vol 66 (4) ◽  
Author(s):  
S. Panigrahi ◽  
R. Basu
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Third Order ◽  
Neutral Differential Equations ◽  
Positive And Negative Coefficients

AbstractIn this paper, the authors study oscillatory and asymptotic behavior of solutions of a class of nonlinear third order neutral differential equations with positive and negative coefficients of the form

On the behavior of solutions of fractional differential equations on time scale via Hilfer fractional derivatives

2018 ◽  
Vol 21 (4) ◽  
pp. 1120-1138 ◽  
Author(s):  
Devaraj Vivek ◽  
Kuppusamy Kanagarajan ◽  
Seenith Sivasundaram
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Uniqueness Of Solutions ◽  
Existence And Stability ◽  
Fractional Differential

Abstract In this paper, we study the existence and stability of Hilfer-type fractional differential equations (dynamic equations) on time scales. We obtain sufficient conditions for existence and uniqueness of solutions by using classical fixed point theorems such as Schauder's fixed point theorem and Banach fixed point theorem. In addition, Ulam stability of the proposed problem is also discussed. As in application, we provide an example to illustrate our main results.

Oscillatory behavior of higher order nonlinear homogeneous neutral delay dynamic equations with positive and negative coefficients

2018 ◽  
Vol 24 (2) ◽  
pp. 139-154
Author(s):  
Saroj Panigrahi ◽  
P. Rami Reddy
Keyword(s):  
Asymptotic Behavior ◽  
Fourth Order ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Oscillatory Behavior ◽  
Dynamic Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Neutral Delay ◽  
Positive And Negative Coefficients ◽  
Delay Dynamic Equations

Abstract In this paper, we derive some sufficient conditions for the oscillatory and asymptotic behavior of solutions of the higher order nonlinear neutral delay dynamic equation with positive and negative coefficients. The results of this paper extend and generalize the results of [S. Panigrahi and P. Rami Reddy, Oscillatory and asymptotic behavior of fourth order non-linear neutral delay dynamic equations, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 20 2013, 143–163] and [S. Panigrahi, J. R. Graef and P. Rami Reddy, Oscillation results for fourth order nonlinear neutral dynamic equations, Commun. Math. Anal. 15 2013, 11–28]. Examples are included to illustrate the validation of the results.

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