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On the "Peano phenomenon" in higher dimensions

The following result in one-dimensional differential equations is sometimes referred to as "Peano phenomenon" (see e.g. here). If $f:\mathbb{R}\to\mathbb{R}$ is a continuous function, the differential …
Todd Chavez's user avatar
3 votes
1 answer
225 views

Existence and uniqueness of solutions for continuous and directionally differentiable ODE

Given $f:\mathbb{R}^n \to \mathbb{R}^n$ continuous and directionally differentiable (i.e., such that the directional derivative of $f$ exists for any direction) at a neighborhood $N$ of $x_0\in\mathbb …
Todd Chavez's user avatar