Projected Gronwall-Bellman's inequality for integrable functions
Without continuity of functions and monotonicity of some functions in Lemma 1, in this paper we discuss a projected Gronwall-Bellman's inequality with only integrability. In the proof of our main result some techniques are applied to overcome difficulties caused by lack of continuity and monotonicity. As applications of our main result we also give estimates in various concrete cases. (C) 2001 Elsevier Science Ltd. All rights reserved.
integrability monotonicity integral inequality differential equation