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Boundedness and periodicity in impulsive ordinary and functional differential equations
Nonlinear Analysis: Theory, Methods & Applications, 2006Periodicity and boundedness are studied for the impulsive ordinary differential equation \[ {\begin{cases} x'(t)=f(t,x),& t\not=t_k,t\geq 0\\ x(t_k)=I_k(x(t_k^-)),&k\in N, \end{cases}} \] and for a similar functional differential equation. Horn's fixed point theorem is applied to establish Hale-Yoshizawa type criteria for the existence of periodic ...
Shen, Jianhua, Li, Jianli, Wang, Qing
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Singular Dirichlet problem for ordinary differential equation with impulses
Nonlinear Analysis: Theory, Methods & Applications, 2006The authors prove existence results for the following impulsive Dirichlet boundary value problem \[ u''(t)=f(t,u(t),u'(t)),\quad u(0)=A, \,\,\, u(T)=B, \] \[ u(t_j+)=I_j(u(t_j)), \,\,\, u'(t_j+)=M_j(u'(t_j)), \,\,\, j=1,\dots,p, \] where \(f\in Car((0,T)\times {\mathbb R}^2),\) \(f\) has time singularities at \(t=0\) and \(t=T,\) \(I_j, M_j\in C^0 ...
Rachůnková, Irena, Tomeček, Jan
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PBVPs for Ordinary Impulsive Differential Equations
2001Impulsive differential equations occur in many biological, physical and engineering applications (see [2 3 5]). In consequence, the study of such systems has gained prominence.
Daniel Franco, Juan J. Nieto
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Fixed mesh approximation of ordinary differential equations with impulses
Numerische Mathematik, 1998An effective algorithm is presented for approximation to the solution of an ordinary differential equation with impulsive forcing function. The system has the form \[ \dot x(t)= f(x(t),t)+ \sum^\infty_{j= 0}\alpha_i \delta(t- t_j),\quad 0\leq t\leq T;\quad x(0)= x_0,\tag{i} \] where \(\sum^\infty_{j= 0}|\alpha_j|< \infty\), and \(f\) is integrable ...
Delfour, Michel, Dubeau, François
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A high-order numerical scheme for the impulsive fractional ordinary differential equations
International Journal of Computer Mathematics, 2017ABSTRACTIn this paper, we use a good technique to construct a high-order numerical scheme for the impulsive fractional ordinary differential equations (IFODEs). This technique is based on the so-called block-by-block method, which is a common method for the integral equations.
Junying Cao, Lizhen Chen, Ziqiang Wang
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Numerical solution of ordinary differential equations with impulse solution
Applied Mathematics and Computation, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Qualitative Theory of Dynamical Systems, 2017
This paper is devoted to the solvability of the following singular boundary value problem with impulsive effects \[ x'(t)=-g(x(t))+e(t), \] \[ \Delta x(t_k)=x(t^+_k)-x(t^-_k)=I_k(x(t_k)),\, k=1,\dots,q, \] \[ x(0)=x(T),\, T>0, \] where \(g:(0,\infty)\to(0,\infty)\) is a continuous and bijective function such that \(\lim_{t\to 0^+}g(t)=+\infty\) and ...
Juan J Nieto
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This paper is devoted to the solvability of the following singular boundary value problem with impulsive effects \[ x'(t)=-g(x(t))+e(t), \] \[ \Delta x(t_k)=x(t^+_k)-x(t^-_k)=I_k(x(t_k)),\, k=1,\dots,q, \] \[ x(0)=x(T),\, T>0, \] where \(g:(0,\infty)\to(0,\infty)\) is a continuous and bijective function such that \(\lim_{t\to 0^+}g(t)=+\infty\) and ...
Juan J Nieto
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Developing Software to Numerically Solve a System of Impulsive Ordinary Differential Equations
Proceedings of the West Virginia Academy of Science, 2020Mathematical models can be used to simulate complex real-world behaviors and provide insights into how these behaviors work. Additionally, these models can be enhanced through complementary software that is able to better manipulate the large sample spaces their parameters tend to have.
BRIAN CRUTCHLEY, Qing Wang
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Mathematische Nachrichten, 2011
AbstractIn this paper, we give sufficient conditions for the uniform boundedness and uniform ultimate boundedness of solutions of a class of retarded functional differential equations with impulse effects acting on variable times. We employ the theory of generalized ordinary differential equations to obtain our results.
Afonso, S. M. +3 more
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AbstractIn this paper, we give sufficient conditions for the uniform boundedness and uniform ultimate boundedness of solutions of a class of retarded functional differential equations with impulse effects acting on variable times. We employ the theory of generalized ordinary differential equations to obtain our results.
Afonso, S. M. +3 more
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PID-type iterative learning control for impulsive ordinary differential equations
Journal of Applied Mathematics and Computing, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gao, Zhuoyan +2 more
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