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Miklós Schweitzer 2003, Problem 7

Source: Miklós Schweitzer 2003

July 30, 2016
college contestsMiklos Schweitzerfunction

Problem Statement

Let rr be a nonnegative continuous function on the real line. Show that there exists a function f∈C1(R)f\in C^1(\mathbb{R}), not identically zero, such that f′(x)=f(x−r(f(x)))f'(x)=f(x-r(f(x))), x∈Rx\in\mathbb{R}.
(translated by L. Erdős)
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