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Boundary value problems for higher order ordinary differential equations with impulses
Nonlinear Analysis: Theory, Methods & Applications, 1998The 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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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, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
François Dubeau +2 more
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Asymptotic equivalence of ordinary and impulsive operator–differential equations
Communications in Nonlinear Science and Numerical Simulation, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Anatoliy A. Martynyuk +2 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, 1985The 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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