Ordinary Differential Equations and Dynamical Systems Vol2 · Problem 3.6

Nonautonomous Linear Systems

Mathematics — Calculus · lipschitz-norm-power

Problem

Show that the function f(x)=∥x∥αf(x) = \|x\|^\alpha, α>0\alpha > 0, from Rn\mathbb{R}^n to R\mathbb{R} is locally Lipschitz continuous if and only if α≥1\alpha \geq 1.

Related theory

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