Results 11 to 20 of about 12,002 (244)
International Journal of Differential Equations, 2019 In this work, we consider an initial value problem of a nonhomogeneous retarded functional equation coupled with the impulsive term. The fundamental matrix theorem is employed to derive the integral equivalent of the equation which is Lebesgue integrable.
D. K. Igobi, U. Abasiekwere
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Oscillation for higher order nonlinear ordinary differential equations with impulses
Electronic Journal of Differential Equations, 2006 In this paper, we study the oscillation of solutions to higher order nonlinear ordinary differential equations with impulses. Several criteria for the oscillations of solutions are given.
Chaolong Zhang, Weizhen Feng
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A Survey on Oscillation of Impulsive Ordinary Differential Equations [PDF]
Advances in Difference Equations, 2010 The authors make a fundamental survey on oscillation of first- and second-order of linear, half-linear, super-half-linear and nonlinear impulse differential equations. The Sturmian theory for second-order linear impulse equations is discussed, too.
Agarwal, Ravi P. +2 more
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Linearization of Impulsive Differential Equations with Ordinary Dichotomy [PDF]
Abstract and Applied Analysis, 2014 This paper presents a linearization theorem for the impulsive differential equations when the linear system has ordinary dichotomy. We prove that when the linear impulsive system has ordinary dichotomy, the nonlinear systemx˙(t)=A(t)x(t)+f(t,x),t≠tk,Δx(tk)=A~(tk)x(tk)+f~(tk,x),k∈ℤ, is topologically conjugated tox˙(t)=A(t)x(t),t≠tk,Δx(tk)=A~(tk)x(tk),k ...
Wong, P. J. Y. +3 more
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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 +2 more
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Impulsive perturbations to differential equations: stable/unstable pseudo-manifolds, heteroclinic connections, and flux [PDF]
, 2016 State-dependent time-impulsive perturbations to a two-dimensional autonomous flow with stable and unstable manifolds are analysed by posing in terms of an integral equation which is valid in both forwards- and backwards-time.
Balasuriya, Sanjeeva
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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. +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 +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 FísicaCommonly, 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 +1 more
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On the genesis of spike-wave oscillations in a mean-field model of human thalamic and corticothalamic dynamics [PDF]
, 2006 In this Letter, the genesis of spike-wave activity—a hallmark of many generalized epileptic seizures—is investigated in a reduced mean-field model of human neural activity.
Breakspear, M, Rodrigues, S, Terry, JR
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