Eine bedingte Form der Integral-Ungleichung von Gronwall, leichte Verallgemeinerung eines Stabilitätssatzes von Perron und überlauffreie Skalierung von Analogrechenschaltungen A conditional version of the integral inequality of gronwall, a slight generalization of a stability theorem of perron, and overflow-free scaling of analogue computer set-ups
This work is motivated by convergence studies of discretization methods for Volterra integral and integro‐differential equations. The results are all given in a form
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[38, Theorem A.43], we obtain. Ff1 − Ff2 Un método iterativo convergente para un sistema logístico quimiotáctico.
If , , and continuous function satisfies the inequalities then A number of different generalizations of Gronwall’s integral inequality with one and two dependent limits have been obtained, see for instance [13, 14]. Generalizations of the classical Gronwall inequality when the kernel of the associated integral equation is weakly singular are presented. The continuous and discrete versions are both given; the former is included since it suggests the latter by analogy. 2004-02-15
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Skunk. Direkte Folgerung aus dem Gronwall{Lemma. Satz: Fur Anfangswerte y 0;z 0 2Rn seien die L osungen y(t;t 0;y 0) und y(t;t 0;z 0) auf dem Intervall jt t 0j "de niert.
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Integral inequalities of Gronwall type have been very useful in the study of ordinary differential equations. Sugiyama [] proved the discrete analogue of the well-known Gronwall-Bellman inequality [2–5] which find numerous applications in the theory of finite difference equations.See [6–11] for differential inequalities and difference inequalities.
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The results are all given in a form This is, of course, the analogue of the method of repeated substitutions used for the continuous case of linear Volterra integral equations, and is essentially the An initial value problem (IVP) for the first-order system is the differential equation We conclude this section with a version of Gronwall's inequality for nonlinear 23 Aug 2020 discrete version of the stochastic Gronwall lemma involving a martingale. the supremum in terms of the infimum for discrete time martingales.