scholarly journals Stability Analysis of Linear Sylvester System of First Order Differential Equations

2020 ◽  
Vol 9 (11) ◽  
pp. 25252-25259
Author(s):  
Kasi Viswanadh V. Kanuri ◽  
SriRam Bhagavathula ◽  
K.N. Murty
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Differential Equations ◽  
Stability Criteria ◽  
Matrix Differential Equation ◽  
Bounded Solutions ◽  
First Order ◽  
Matrix Differential ◽  
First Order Differential Equations

    In this paper, we establish stability criteria of the linear Sylvester system of matrix differential equation using the new concept of bounded solutions and deduce the existence of -bounded solutions as a particular case.

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

scholarly journals ON CONDITIONING FOR A GENERAL SYSTEM OF FOUR POINT BOUNDARY VALUE PROBLEMS

1996 ◽  
Vol 27 (3) ◽  
pp. 219-225
Author(s):  
M. S. N. MURTY
Keyword(s):  
Differential Equation ◽  
Fundamental Matrix ◽  
Close Relationships ◽  
General System ◽  
Point Boundary ◽  
Matrix Differential Equation ◽  
Growth Behaviour ◽  
First Order ◽  
Matrix Differential ◽  
The Stability

In this paper we investigate the close relationships between the stability constants and the growth behaviour of the fundamental matrix to the general FPBVP'S associated with the general first order matrix differential equation.

Ladder operators and a differential equation for varying generalized Freud-type orthogonal polynomials

2018 ◽  
Vol 07 (04) ◽  
pp. 1840005 ◽  
Author(s):  
Galina Filipuk ◽  
Juan F. Mañas-Mañas ◽  
Juan J. Moreno-Balcázar
Keyword(s):  
Differential Equation ◽  
Difference Equation ◽  
Differential Equations ◽  
Orthogonal Polynomials ◽  
Inner Product ◽  
Ladder Operators ◽  
First Order ◽  
Standard Family ◽  
Differential Difference Equation ◽  
First Order Differential Equations

In this paper, we introduce varying generalized Freud-type polynomials which are orthogonal with respect to a varying discrete Freud-type inner product. Our main goal is to give ladder operators for this family of polynomials as well as find a second-order differential–difference equation that these polynomials satisfy. To reach this objective, it is necessary to consider the standard Freud orthogonal polynomials and, in the meanwhile, we find new difference relations for the coefficients in the first-order differential equations that this standard family satisfies.

scholarly journals Oscillation Criteria for First Order Differential Equations with Non-Monotone Delays

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 718 ◽  
Author(s):  
Emad R. Attia ◽  
Hassan A. El-Morshedy ◽  
Ioannis P. Stavroulakis
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Oscillation Criteria ◽  
Lower Upper ◽  
First Order ◽  
Upper Limit ◽  
First Order Differential Equations

New sufficient criteria are obtained for the oscillation of a non-autonomous first order differential equation with non-monotone delays. Both recursive and lower-upper limit types criteria are given. The obtained results improve most recent published results. An example is given to illustrate the applicability and strength of our results.

scholarly journals Existence of Ψ Bounded Solutions for a Lyapunov Matrix Dierential Equation

2014 ◽  
Vol 52 (2) ◽  
Author(s):  
Aurel Diamandescu
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Bounded Solution ◽  
Sufficient Condition ◽  
Matrix Differential Equation ◽  
Bounded Solutions ◽  
Necessary And Sufficient Condition ◽  
Lyapunov Matrix ◽  
Matrix Differential ◽  
Necessary And Sufficient

AbstractIt is proved a necessary and sufficient condition for the existence of at least one Ψ- bounded solution of a linear non- homogeneous Lyapunov matrix differential equation. In addition, it is given a result in connection with the asymptotic behavior of the Ψ- bounded solutions of this equation.

scholarly journals Fractional differential equation with uncertainty

2021 ◽  
Vol 23 (08) ◽  
pp. 181-185
Author(s):  
Karanveer Singh ◽  
◽  
R N Prajapati ◽  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Fractional Order ◽  
Order Differential Equation ◽  
Fractional Order Differential Equation ◽  
First Order ◽  
Fractional Differential ◽  
First Order Differential Equations

We consider a fractional order differential equation with uncertainty and introduce the concept of solution. It goes beyond ordinary first-order differential equations and differential equations with uncertainty.

On matrix differential equations with several unbounded delays

2006 ◽  
Vol 17 (4) ◽  
pp. 417-433 ◽  
Author(s):  
J. ĈERMÁK
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Equation ◽  
Matrix Differential Equation ◽  
Continuous Vector ◽  
Asymptotic Bounds ◽  
The Matrix ◽  
Exponentially Stable ◽  
Matrix Differential Equations ◽  
Matrix Differential

The paper focuses on the matrix differential equation \[ \dot y(t)=A(t)y(t)+\sum_{j=1}^{m}B_j(t)y(\tau_j(t))+f(t),\quad t\in I=[t_0,\infty)\vspace*{-3pt} \] with continuous matrices $A$, $B_j$, a continuous vector $f$ and continuous delays $\tau_j$ satisfying $\tau_k\circ\tau_l =\tau_l\circ\tau_k$ on $I$ for any pair $\tau_k,\tau_l$. Assuming that the equation \[ \dot y(t)=A(t)y(t)\] is uniformly exponentially stable, we present some asymptotic bounds of solutions $y$ of the considered delay equation. A system of simultaneous Schröder equations is used to formulate these asymptotic bounds.

scholarly journals EXISTENCE RESULTS AND STABILITY CRITERIA FOR ABC-FUZZY-VOLTERRA INTEGRO-DIFFERENTIAL EQUATION

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040048 ◽  
Author(s):  
HASIB KHAN ◽  
J. F. GOMEZ-AGUILAR ◽  
THABET ABDELJAWAD ◽  
AZIZ KHAN
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Ulam Stability ◽  
Stability Criteria ◽  
Science And Engineering

In the modeling of dynamical problems the fractional order integro-differential equations (IDEs) are very common in science and engineering. The scientists are developing different aspects of these models. The existence of solutions, stability analysis and numerical simulations are the most commonly studied aspects. There is no paper in literature describing the Hyers–Ulam stability (HU-stability) for fuzzy-fractional order models. Therefore, keeping the importance of the study, we consider the existence, uniqueness and HU-stability of a fractional order fuzzy-Volterra IDE.

Oscillation of first-order differential equations with several non-monotone retarded arguments

2020 ◽  
Vol 27 (3) ◽  
pp. 341-350 ◽  
Author(s):  
Huseyin Bereketoglu ◽  
Fatma Karakoc ◽  
Gizem S. Oztepe ◽  
Ioannis P. Stavroulakis
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Order Linear Differential Equation ◽  
Oscillation Criteria ◽  
Order Linear ◽  
First Order ◽  
Linear Differential ◽  
First Order Differential Equations

AbstractConsider the first-order linear differential equation with several non-monotone retarded arguments {x^{\prime}(t)+\sum_{i=1}^{m}p_{i}(t)x(\tau_{i}(t))=0}, {t\geq t_{0}}, where the functions {p_{i},\tau_{i}\in C([t_{0},\infty),\mathbb{R}^{+})}, for every {i=1,2,\ldots,m}, {\tau_{i}(t)\leq t} for {t\geq t_{0}} and {\lim_{t\to\infty}\tau_{i}(t)=\infty}. New oscillation criteria which essentially improve the known results in the literature are established. An example illustrating the results is given.

On the Oscillation of Solutions of First Order Differential Equations with Retarded Arguments

2003 ◽  
Vol 10 (1) ◽  
pp. 63-76 ◽  
Author(s):  
M. K. Grammatikopoulos ◽  
R. Koplatadze ◽  
I. P. Stavroulakis
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Integral Conditions ◽  
First Order ◽  
All Solutions ◽  
Oscillation Of Solutions ◽  
First Order Differential Equations

Abstract For the differential equation where 𝑝𝑖 ∈ 𝐿 loc (𝑅+; 𝑅+), τ 𝑖 ∈ 𝐶(𝑅+; 𝑅+), τ 𝑖(𝑡) ≤ 𝑡 for 𝑡 ∈ 𝑅+, , optimal integral conditions for the oscillation of all solutions are established.

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