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Prolongation of solutions of measure differential equations and dynamic equations on time scales
Author(s) -
Federson M.,
Grau R.,
Mesquita J. G.
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201700420
Subject(s) - mathematics , measure (data warehouse) , uniqueness , mathematical analysis , ordinary differential equation , differential equation , numerical partial differential equations , dynamic equation , differential algebraic equation , independent equation , nonlinear system , computer science , physics , database , quantum mechanics
In this paper, we prove the results on existence and uniqueness of the maximal solutions for measure differential equations, considering more general conditions on functions f and g by using the correspondence between the solutions of these equations and the solutions of generalized ODEs. Moreover, we prove these results for the dynamic equations on time scales, using the correspondence between the solutions of these last equations and the solutions of the measure differential equations.