Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Keywords

  • Peano
  • ordinary differential equations
  • Peano's existence theorem
  • differential inequalities
  • Grönwall-type inequalities
  • strict sub-solutions
  • strict super-solutions
  • sub-solution method
  • super-solution method
  • maximum solution
  • minimum solution
  • continuously differentiable function
  • Weierstrass maximum theorem

Mathematics Subject Classification

01A55, 34A12, 34A40

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Suggested citation

G. H. Greco, S. Mazzucchi. “The Originality of Peano's 1886 Existence Theorem on Scalar Differential Equations.” Journal of Convex Analysis 23 (2016), No. 3, 649–659. https://doi.org/10.68381/jca23025

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Published by Heldermann Verlag, 2016. Rights now held by Banach Press.