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

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.