A note on the theorem of Lakshmikantham and Leela

摘要

We study the initial value problem u′ = f(t, u), u(0) = u0, in a real Banach space. Using the fixed point principle of Daher and the theorem of Mönch and von Harten, we obtain a theorem which is an extension of that established by Lakshmikantham and Leela in [1].