Optimal version of the Picard–Lindelöf theorem
- 1 January 2021
- journal article
- research article
- Published by University of Szeged in Electronic Journal of Qualitative Theory of Differential Equations
- No. 39,p. 1-8
- https://doi.org/10.14232/ejqtde.2021.1.39
Abstract
Consider the differential equation y' = F(x, y). We determine the weakest possible upper bound on vertical bar F(x,y) - F(x,z)vertical bar which guarantees that this equation has for all initial values a unique solution, which exists globally.Keywords
This publication has 5 references indexed in Scilit:
- A note on Cauchy-Lipschitz-Picard theoremJournal of Inequalities and Applications, 2016
- A generalized Picard-Lindelöf theoremElectronic Journal of Qualitative Theory of Differential Equations, 2016
- Integration by Parts and by Substitution Unified with Applications to Green's Theorem and Uniqueness for ODEsThe American Mathematical Monthly, 2016
- An extension of picard-lindelöff theorem to fractional differential equations*Applicable Analysis, 1998
- Nonuniqueness and Growth in First-Order Differential EquationsThe American Mathematical Monthly, 1982