AN ASYMPTOTIC STABILITY THEOREM FOR QUASILINEAR DELAY DIFFERENTIAL EQUATIONS WITH OSCILLATING COEFFICIENTS

2013 ◽  
Vol 24 (11) ◽  
pp. 1350092 ◽  
Author(s):  
NGUYEN TIEN DUNG
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Asymptotic Behavior Of Solutions ◽  
Variable Delays ◽  
Nonlinear Anal ◽  
Oscillating Coefficients ◽  
Several Delays

In this paper, we provide new necessary and sufficient conditions of the asymptotic stability for a class of quasilinear differential equations with several delays and oscillating coefficients. Our results are established by means of fixed point theory and improve those obtained in [J. R. Graef, C. Qian and B. Zhang, Asymptotic behavior of solutions of differential equations with variable delays, Proc. London Math. Soc.81 (2000) 72–92; B. Zhang, Fixed points and stability in differential equations with variable delays, Nonlinear Anal.63 (2005) e233–e242].

scholarly journals FIXED POINTS AND STABILITY OF A CLASS OF NONLINEAR DELAY INTEGRO-DIFFERENTIAL EQUATIONS WITH VARIABLE DELAYS

2017 ◽  
pp. 031
Author(s):  
Hocine Gabsi ◽  
Abdelouaheb Ardjouni ◽  
Ahcene Djoudi
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Fixed Point Theory ◽  
Zero Solution ◽  
Point Theory ◽  
Second Order ◽  
Asymptotically Stable ◽  
Variable Delays ◽  
Nonlinear Delay

In this work we study a class of second order nonlinear neutral integro-differential equations    x(t)+f(t,x(t),x(t))x(t)+∑_{j=1}^{N}∫_{t-τ_{j}(t)}^{t}a_{j}(t,s)g_{j}(s,x(s))ds    +∑_{j=1}^{N}b_{j}(t)x′(t-τ_{j}(t))=0,with variable delays and give some new conditions ensuring that the zero solution is asymptotically stable by means of the fixed point theory. Our work extends and improves previous results in the literature such as, D. Pi <cite>pi2,pi3</cite> and T. A. Burton <cite>b12</cite>. An example is given to illustrate our claim.

scholarly journals Asymptotic Stability of Impulsive Cellular Neural Networks with Infinite Delays via Fixed Point Theory

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Yutian Zhang ◽  
Yuanhong Guan
Keyword(s):  
Neural Networks ◽  
Fixed Point ◽  
Asymptotic Stability ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Cellular Neural Networks ◽  
Infinite Delays ◽  
Trivial Equilibrium ◽  
The Stability

We employ the new method of fixed point theory to study the stability of a class of impulsive cellular neural networks with infinite delays. Some novel and concise sufficient conditions are presented ensuring the existence and uniqueness of solution and the asymptotic stability of trivial equilibrium at the same time. These conditions are easily checked and do not require the boundedness and differentiability of delays.

scholarly journals Necessary and Sufficient Conditions for Oscillatory and Asymptotic Behaviour of Solutions to Second-Order Nonlinear Neutral Differential Equations with Several Delays

2020 ◽  
Vol 75 (1) ◽  
pp. 121-134 ◽  
Author(s):  
Shyam Sundar Santra
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Main Tool ◽  
Second Order ◽  
Necessary And Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
Several Delays ◽  
Necessary And Sufficient

AbstractIn this paper, necessary and sufficient conditions are obtained for oscillatory and asymptotic behavior of solutions to second-order nonlinear neutral delay differential equations of the form {d \over {dt}}\left[ {r\left( t \right){{\left[ {{d \over {dt}}\left( {x\left( t \right) + p\left( t \right)x\left( {t - \tau } \right)} \right)} \right]}^\alpha }} \right] + \sum\limits_{i = 1}^m {{q_i}\left( t \right)H\left( {x\left( {t - {\sigma _i}} \right)} \right) = 0\,\,\,{\rm{for}}\,t \ge {t_0} > 0,}under the assumption ∫∞(r(n))−1/αdη=∞. Our main tool is Lebesque’s dominated convergence theorem. Further, some illustrative examples showing the applicability of the new results are included.

scholarly journals On a nonlinear system of Riemann-Liouville fractional differential equations with semi-coupled integro-multipoint boundary conditions

2021 ◽  
Vol 19 (1) ◽  
pp. 760-772
Author(s):  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Badrah Alghamdi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Nonlinear System ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Numerical Examples ◽  
Multipoint Boundary ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential

Abstract We study a nonlinear system of Riemann-Liouville fractional differential equations equipped with nonseparated semi-coupled integro-multipoint boundary conditions. We make use of the tools of the fixed-point theory to obtain the desired results, which are well-supported with numerical examples.

scholarly journals Second-order impulsive differential systems with mixed and several delays

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shyam Sundar Santra ◽  
Apurba Ghosh ◽  
Omar Bazighifan ◽  
Khaled Mohamed Khedher ◽  
Taher A. Nofal
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Oscillation Theory ◽  
Second Order ◽  
Neutral Delay ◽  
Differential Systems ◽  
Impulsive Differential Systems ◽  
Several Delays ◽  
Necessary And Sufficient

AbstractIn this work, we present new necessary and sufficient conditions for the oscillation of a class of second-order neutral delay impulsive differential equations. Our oscillation results complement, simplify and improve recent results on oscillation theory of this type of nonlinear neutral impulsive differential equations that appear in the literature. An example is provided to illustrate the value of the main results.

scholarly journals Existence results for coupled nonlinear fractional differential equations of different orders with nonlocal coupled boundary conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ahmed Alsaedi ◽  
Soha Hamdan ◽  
Bashir Ahmad ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Arbitrary Domain ◽  
Uniqueness Of Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Coupled Boundary Conditions ◽  
Fractional Differential

AbstractThis paper is concerned with the solvability of coupled nonlinear fractional differential equations of different orders supplemented with nonlocal coupled boundary conditions on an arbitrary domain. The tools of the fixed point theory are applied to obtain the criteria ensuring the existence and uniqueness of solutions of the problem at hand. Examples illustrating the main results are presented.

scholarly journals Existence results of ψ-Hilfer integro-differential equations with fractional order in Banach space

2020 ◽  
Vol 19 (1) ◽  
pp. 171-192
Author(s):  
Mohammed A. Almalahi ◽  
Satish K. Panchal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Banach Fixed Point Theorem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Mönch Fixed Point Theorem

AbstractIn this article we present the existence and uniqueness results for fractional integro-differential equations with ψ-Hilfer fractional derivative. The reasoning is mainly based upon different types of classical fixed point theory such as the Mönch fixed point theorem and the Banach fixed point theorem. Furthermore, we discuss Eα -Ulam-Hyers stability of the presented problem. Also, we use the generalized Gronwall inequality with singularity to establish continuous dependence and uniqueness of the δ-approximate solution.

Coupled fractional differential systems with random effects in Banach spaces

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
O. Zentar ◽  
M. Ziane ◽  
S. Khelifa
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Random Differential Equations ◽  
Liouville Fractional Derivative ◽  
Fractional Differential ◽  
Vector Valued ◽  
Abstract Formulation

Abstract The purpose of this work is to investigate the existence of solutions for a system of random differential equations involving the Riemann–Liouville fractional derivative. The existence result is established by means of a random abstract formulation to Sadovskii’s fixed point theorem principle [A. Baliki, J. J. Nieto, A. Ouahab and M. L. Sinacer, Random semilinear system of differential equations with impulses, Fixed Point Theory Appl. 2017 2017, Paper No. 27] combined with a technique based on vector-valued metrics and convergent to zero matrices. An example is also provided to illustrate our result.

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