On the Cauchy problem for first order discontinuous ordinary differential equations

DOI10.1006/jmaa.2001.7642zbMath1003.34008OpenAlexW1976533388MaRDI QIDQ5956513

Rodrigo López Pouso

Publication date: 12 January 2003

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.2001.7642

zbMATH Keywords

existenceextremal solutionsdiscontinuous right-hand side

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Discontinuous ordinary differential equations (34A36)

Related Items (10)

Uniqueness and existence results for ordinary differential equations ⋮ Existence of solutions of first-order differential equations via a fixed point theorem for discontinuous operators ⋮ Some qualitative properties of solutions of higher-order lower semicontinus differential inclusions ⋮ On uniqueness for some non-Lipschitz SDE ⋮ Schauder's fixed-point theorem: new applications and a new version for discontinuous operators ⋮ Extremal solutions of measure differential equations ⋮ On extending existence theory from scalar ordinary differential equations to infinite quasimonotone systems of functional equations ⋮ Computability on reals, infinite limits and differential equations ⋮ Unnamed Item ⋮ On first-order ordinary differential equations with nonnegative right-hand sides

Cites Work

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• Subfunctions and the initial-value problem for differential equations satisfying Caratheodory's hypotheses
• Existence of solutions for discontinuous differential equations
• One-dimensional differential equations under weak assumptions
• Existence, uniqueness, and comparison results for a differential equation with discontinuous nonlinearities
• Integration in linear spaces
• Continuous Dependence of Nonmonotonic Discontinuous Differential Equations
• Extremal solutions of a discontinuous scalar differential equation
• A unified theory for first-order discontinuous scalar differential equations

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