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Journal of Convex Analysis 23 (2016), No. 3, 649--659
Copyright Heldermann Verlag 2016

The Originality of Peano's 1886 Existence Theorem on Scalar Differential Equations

Gabriele H. Greco
Via Cesarini 27/2, 38121 Trento, Italy

Sonia Mazzucchi
Dip. di Matematica, Università di Trento, via Sommarive 14, 38123 Povo, Italy

The paper presents a revisited proof of Peano's existence theorem, emphasizing the historical background. The argument relies on methods and results due to Peano, such as comparison theorems by differential inequalities, Grönwall-type inequalities, sub- and super-solutions, maximum and minimum solutions, a characterization of continuously differentiable functions and Weierstrass maximum theorem for functions of several variables.

Keywords: Peano, ordinary differential equations, Peano's existence theorem, differential inequalities, Groenwall-type inequalities; strict sub-solutions, strict super-solutions, sub-solution method, super-solution-method, maximum solution, minimum solution, con

MSC: 01A55, 34A12, 34A40

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