Ordinary Differential Equations and Dynamical Systems Vol2 · Problem 3.5

Nonautonomous Linear Systems

Mathematics — Calculus · lipschitz-continuity-properties

Problem

Let Ω⊂Rn\Omega \subset \mathbb{R}^n be an open set. Suppose that f:Ω→Rnf : \Omega \to \mathbb{R}^n. (a) Prove that if ff is locally Lipschitz continuous on Ω\Omega, then it is continuous on Ω\Omega. (b) Prove that if ff is continuously differentiable on Ω\Omega, then it is locally Lipschitz on Ω\Omega.

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