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On démontre ici un lemme de Hensel pour les opérateurs différentiels. On en déduit un
théorème de factorisation pour des opérateurs différentiels à coefficients dans une
extension liouvillienne transcendante d’un corps valué. On obtient en particulier un
théorème de factorisation pour des opérateurs différentiels à coefficients dans une
extension de par un nombre fini d’exponentielles et de logarithmes
algébriquement indépendants sur .
A new class of fractional linear continuous-time linear systems described by state equations is introduced. The solution to the state equations is derived using the Laplace transform. Necessary and sufficient conditions are established for the internal and external positivity of fractional systems. Sufficient conditions are given for the reachability of fractional positive systems.
The error analysis of preconditioned waveform relaxation iterations for differential systems is presented. This analysis extends and refines previous results by Burrage, Jackiewicz, Nørsett and Renaut by incorporating all terms in the expansion of the error of waveform relaxation iterations in the Laplace transform domain. Lower bounds for the size of the window of rapid convergence are also obtained. The theory is illustrated for waveform relaxation methods applied to differential systems resulting...
Suppose that the function in the differential equation (1) is decreasing on where . We give conditions on which ensure that (1) has a pair of solutions such that the -th derivative () of the function has the sign for sufficiently large and that the higher differences of a sequence related to the zeros of solutions of (1) are ultimately regular in sign.
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