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Some observations on a Conti's result

Adrian Constantin (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

An extension of a result of R. Conti is given from which some integro-differential inequalities of the Gronwall-Bellman-Bihari type and a criterion for the continuation of solutions of a system of ordinary differential equations are deduced.

Some remarks on comparison functions

Antoni Augustynowicz (2009)

Annales Polonici Mathematici

We answer some questions concerning Perron and Kamke comparison functions satisfying the Carathéodory condition. In particular, we show that a Perron function multiplied by a constant may not be a Perron function, and that not every comparison function is bounded by a comparison function with separated variables. Moreover, we investigate when a sum of Perron functions is a Perron function. We also present a criterion for comparison functions with separated variables.

Some remarks on Nagumo's theorem

Thomas Mejstrik (2012)

Czechoslovak Mathematical Journal

We provide a simpler proof for a recent generalization of Nagumo’s uniqueness theorem by A. Constantin: On Nagumo’s theorem. Proc. Japan Acad., Ser. A 86 (2010), 41–44, for the differential equation x ' = f ( t , x ) , x ( 0 ) = 0 and we show that not only is the solution unique but the Picard successive approximations converge to the unique solution. The proof is based on an approach that was developed in Z. S. Athanassov: Uniqueness and convergence of successive approximations for ordinary differential equations. Math....

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