A uniqueness criterion for ordinary differential equations
Adrian Constantin
Abstract
We show that a convex combination of the Nagumo and Osgood growth conditions for the spatial variation of continuous functions ensures the uniqueness of the solution to the initial-value problem for the associated ordinary differential equation. Moreover, this unique solution is obtained as the uniform limit of the sequence of successive approximations.
Topics & Concepts
MathematicsUniquenessOrdinary differential equationLimit (mathematics)Mathematical analysisRegular polygonInitial value problemSequence (biology)Applied mathematicsDifferential equationGeneticsGeometryBiologyAdvanced Mathematical Modeling in EngineeringNonlinear Differential Equations AnalysisNonlinear Partial Differential Equations