Abstract

The Gronwall - Bellman’s Lemma (GBL) plays very important role in the researching Quality Theory of Ordinary Differential Equations. Beside the GBL there are many expansions, that was gave by some the authors, example Brézis[3], Bihari [2],... This report has investigated two problems : Expansions and Applications of this important lemma. The special new results are given by the lemmas 6, 9 and many theorems for applied case, example the theorems 4, 5, 6 about stablity of similar control system.