Geodesic
The Originality of Peano's 1886 Existence Theorem on Scalar Differential Equations
Journal of convex analysis, Tome 23 (2016) no. 3, pp. 649-659
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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.
Classification : 01A55, 34A12, 34A40
Mots-clés : 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 
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     author = {G. H. Greco and S. Mazzucchi},
     title = {The {Originality} of {Peano's} 1886 {Existence} {Theorem} on {Scalar} {Differential} {Equations}},
     journal = {Journal of convex analysis},
     pages = {649--659},
     year = {2016},
     volume = {23},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2016_23_3_JCA_2016_23_3_a1/}
}
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G. H. Greco; S. Mazzucchi. The Originality of Peano's 1886 Existence Theorem on Scalar Differential Equations. Journal of convex analysis, Tome 23 (2016) no. 3, pp. 649-659. http://geodesic.mathdoc.fr/item/JCA_2016_23_3_JCA_2016_23_3_a1/