Results 11 to 20 of about 684 (224)

A BLOCK-BY-BLOCK METHOD FOR THE IMPULSIVE FRACTIONAL ORDINARY DIFFERENTIAL EQUATIONS

Journal of Applied Analysis & Computation, 2020
Summary: In this paper, a block-by-block numerical method is constructed for the impulsive fractional ordinary differential equations (IFODEs). Firstly, the stability and convergence analysis of the scheme are established. Secondly, the numerical solution which converges to the exact solution with order \(3+\gamma\) for \(0 < \gamma < 1\), where ...
Cao, Junying, Chen, Lizhen, Wang, Ziqiang   +2 more
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Eventual stability and eventual boundedness for impulsive differential equations with “supremum”

Mathematical Modelling and Analysis, 2011
Eventual stability and eventual boundedness for nonlinear impulsive differential equations with supremums are studied. The impulses take place at fixed moments of time. Piecewise continuous Lyapunov functions have been applied.
Ivanka Stamova
doaj   +1 more source

On the existence of periodic solution of some quasilinear differential equations with impulses

Vietnam Journal of Mechanics, 2004
As for ordinary differential equations, one of the problems that especially attract the attention of many mathematicians is the problem on the existence of periodic solutions of the differential equation systems with impulses.
Le Luong Tai
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Multiple Periodic Solutions and Fractal Attractors of Differential Equations with n-Valued Impulses

Mathematics, 2020
Ordinary differential equations with n-valued impulses are examined via the associated Poincaré translation operators from three perspectives: (i) the lower estimate of the number of periodic solutions on the compact subsets of Euclidean spaces and, in ...
Jan Andres
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On nonclassical impulsive ordinary differential equations with nonlocal conditions

International Journal of Analysis and Applications, 2019
Summary: Results on mild solutions of nonclassical differential equations with impulsive and nonlocal conditions are extended to a case when the nonlocal conditions are necessarily non Lipschitz and non compact.
Bishop, S.A., Agarana, M. C., Oghonyon, J. G.   +2 more
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Ulam’s type stability of impulsive ordinary differential equations

Journal of Mathematical Analysis and Applications, 2012
The authors consider the following impulsive differential equations \[ x'(t)= f(t,x(t)),\quad t\in J':= J\setminus\{t_1,\dotsc, t_m\},\quad J:= [0,T],\;T> 0, \] \[ \Delta x(t_k)= I_k(x(t^-_k)),\quad k= 1,2,\dotsc, m, \] where \(f: J\times\mathbb{R}\to \mathbb{R}\) is continuous, \(I_k: \mathbb{R}\to \mathbb{R}\), \(T< \infty\), and \[ x(t^+_k)= \lim_ ...
Wang, JinRong, Fec˘kan, Michal, Zhou, Yong   +2 more
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Some applications of Laplace transforms in models with impulses or discontinuous forcing functions [PDF]

Revista Brasileira de Ensino de Física
Commonly, in Ordinary Differential Equations courses, equations with impulses or discontinuous forcing functions are studied. In this context, the Laplace Transform of the Dirac delta function and unit step function is taught, which are used as forcing ...
Diego Miranda Gonçalves, Lucas Antonio Caritá   +1 more
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Controllability of nonlinear ordinary differential equations with non-instantaneous impulses

Mathematical Modelling and Control, 2022
<abstract><p>In this paper, we consider controllability of the initial value problem with non-instantaneous impulse on ordered Banach spaces. We firstly give a solution expression for initial value problems with non-instantaneous impulses in ordered Banach Spaces by using Schauder fixed point theorem.
Zhen Xin, Yuhe Yang, Qiaoxia Li
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Impulsive system of ODEs with general linear boundary conditions

Electronic Journal of Qualitative Theory of Differential Equations, 2013
The paper provides an operator representation for a problem which consists of a system of ordinary differential equations of the first order with impulses at fixed times and with general linear boundary conditions \begin{gather} z'(t) = A(t)z(t) + f(t,z ...
Irena Rachůnková, Jan Tomeček
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Oscillations of second-order nonlinear impulsive ordinary differential equations

Journal of Computational and Applied Mathematics, 2003
The authors study the second-order impulsive ordinary differential equation \[ \left(r(t)\bigl(x'(t)\bigr)^\sigma \right)'+f(t,x(t))=0, \qquad t\geq t_0, \;t\neq t_k, \;k=1,2,\dots \eqno(1) \] where \(r\in C({\mathbb R}, (0,\infty))\), \(f\in C({\mathbb R}\times {\mathbb R}, {\mathbb R})\) and \(f\) satisfies the sign condition \(xf(t,x)>0\) for all ...
He, Zhimin, Ge, Weigao
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