On the cauchy problem for first order discontinous ordinary differential equations

Abstract

We prove the existence of extremal Carathéodory solutions for the initial value problem x′(t) = f(t, x(t)) for a.e. t ε [0, 1], x(0) = 0, under weak conditions over f: [0, 1] × ℝ → ℝ. © 2001 Elsevier Science.