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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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Galerkin Methods for Nonlinear Ordinary Differential Equation with Impulses
Numerical Algorithms, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dubeau, F., Ouansafi, A., Sakat, A.
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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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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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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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