A note on the theorem of Lakshmikantham and Leela |
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| Institution: | 1. School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan 410083, China;2. School of Mathematical Sciences, CMA-Shanghai, Shanghai Jiao Tong University, Shanghai, 200240, China;1. Lomonosov Moscow State University, Faculty of Physics, Vorob''jovy Gory, Moscow, 19899, Russia;2. Humboldt University of Berlin, Institute of Mathematics, Rudower Chaussee 25, Berlin, 12489, Germany;3. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, Berlin, 10117, Germany |
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| Abstract: | 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]. |
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