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A note on Gronwall-Bellman inequality. (English) Zbl 0274.45011

MSC:
45M10 Stability theory for integral equations
45M99 Qualitative behavior of solutions to integral equations
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References:
[1] Bellman, R, Stability theory of differential equations, (1953), McGraw-Hill New York · Zbl 0052.31505
[2] Chandra, J; Fleishman, B.A, On a generalization of the Gronwall-Bellman lemma in partially ordered Banach spaces, J. math. anal. appl., 31, 668-681, (1970) · Zbl 0179.20302
[3] Coddington, E.A; Levinson, N, Theory of ordinary differential equations, (1955), McGraw-Hill New York · Zbl 0042.32602
[4] Gronwall, T.H, Note on the derivatives with respect to a parameter of the solutions of a system of differential equations, Ann. math., 20, 292-296, (1919) · JFM 47.0399.02
[5] Lakshmikantham, V, A variation of constants formula and Bellman-Gronwall-reid inequalities, J. math. anal. appl., 41, 199-204, (1973) · Zbl 0251.34009
[6] Rao, M.Rama Mohana; Tsokos, C.P, Integrodifferential equations of Volterra type, Bull. austral. math. soc., 3, 9-22, (1970) · Zbl 0201.44002
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