Open Access Open Access  Restricted Access Subscription or Fee Access

Filippov-Gronwall Inequality for Discontinuous Differential Inclusions

Georgi Smirnov, Francisco Miranda

Abstract


We prove two versions of the Filippov-Gronwall inequality for differential inclusions with upper semi-continuous right-hand side. The proof of one theorem is based on monotonicity ideas and the other result is deduced from the Kakutani fixed-point theorem. The first theorem is applied to get some sufficient condition of an equilibrium position weak asymptotic stability, and the second one is used to describe tangent vectors to the solution set of a discontinuous differential inclusion.

Full Text:

PDF


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.