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

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.