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Boundedness of solutions of retarded functional differential equations with variable impulses via generalized ordinary differential equations [PDF]

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., Bonotto, E. M., Federson, M., Gimenes, L. P.   +3 more
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Boundary value problems for higher order ordinary differential equations with impulses

Nonlinear Analysis: Theory, Methods & Applications, 1998
The authors use the method of upper and lower solutions coupled with a monotone iterative technique, to study existence and approximation of solutions to some boundary value problems for higher-order ordinary differential equations with impulses of the type \[ u^{(n)}(t) = f(t,u(t)), \text{ for } \;a.e.
Cabada, Alberto, Liz, Eduardo
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Positive Periodic Solutions for a First Order Singular Ordinary Differential Equation Generated by Impulses

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, José M. Uzal
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Galerkin Methods for Nonlinear Ordinary Differential Equation with Impulses

Numerical Algorithms, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
François Dubeau, Abdelatif Ouansafi, A. Sakat   +2 more
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Asymptotic equivalence of ordinary and impulsive operator–differential equations

Communications in Nonlinear Science and Numerical Simulation, 2019
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Anatoliy A. Martynyuk, Gani Tr. Stamov, Ivanka M. Stamova   +2 more
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Systems of differential equations with implicit impulses and fully nonlinear boundary conditions [PDF]

Boundary Value Problems, 2013
We show that systems of second-order ordinary differential equations, x′ = f (t, x, x″), subject to compatible nonlinear boundary conditions and impulses, have a solution x such that (t, x(t)) lies in an admissible bounding subset of [0, 1] × ℝ when f ...
Song, Yawei, Bevan Thompson, Yawei Song, Thompson, Bevan   +3 more
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INTEGRAL SURFACES FOR HYPERBOLIC ORDINARY DIFFERENTIAL EQUATIONS WITH IMPULSES

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, 1985
The paper considers integral surfaces of systems of differential equations with impulse perturbations at fixed moments of time. Sufficient conditions have been obtained for the existence of integral surfaces with definite properties and the behaviour of the solutions has been studied with initial conditions outside these surfaces.
Hristova, S. G., Bainov, D. D.
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On Impulsive Ordinary and Delay Differential Equations

2002
Existence and uniqueness of the solution to ordinary and delay differential equations with infinitely many state-dependent impulses are considered. A simple transformation allows us to show that these problems are equivalent to problems without impulse. A fixed point approach is then applied for an appropriate norm.
François Dubeau, Jamila Karrakchou, Abdellatif Ouansafi, Abdeljalil Sakat   +3 more
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PBVPs for Ordinary Impulsive Differential Equations

2001
Impulsive 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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Ordinary dichotomy and perturbations of the impulse matrices of linear impulsive differential equation

International Journal of Theoretical Physics, 1990
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Milev, N. V., Bajnov, D. D.
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