Gronwall T H. Note on the derivatives with respect to a parameter of the solutions of a system of differential equations[J]. Ann Math,1919,20(4):292-296.
[2]
Bellman R. The stability of solutions of linear differential equations[J]. Duke Math J,1943,10:643-647.
[3]
Bihari I. A generalization of a lemma of Bellman and its application to uniqueness problems of differential equations[J]. Acta Math Acad Sci Hang,1956,7:81-94.
[4]
Pachpatte B G. A note on Gronwall-Bellman inequality[J]. J Math Anal Appl,1973,44:758-762.
[5]
Lipovan O. A retarded Gronwall-like inequality and its applications[J]. J Math Anal Appl,2000,252(1):389-401.
[6]
Agarwal R P, Deng S, Zhang W. Generalization of a retarded Gronwall-like inequality and its applications[J]. Appl Math Comput,2005,165(3):599-612.
[7]
Dannan F. Integral inequalities of Gronwall-Bellman-Bihari type and asymptotic behavior of certain second order nonlinear differential equations[J]. J Math Anal Appl,1985,108(1):151-164.
[8]
Pachpatte B G. On some generalization of Bellman’s lemma[J]. J Math Anal Appl,1975,51:141-150.
[9]
Samoilenko A M, Perestjuk N A. Stability of the solutions of differential equations with impulsive action[J]. Diff Urav,1977,13:1981-1992.
[10]
Borysenko D S. About one Integral Inequality for Piece-wise Continuous Functions[C]//Proc.X Int. Kravchuk Conf,Kyiv,2004:323.
[11]
Iovane G. Some new integral inequalities of Bellman-Bihari type with delay for discontinuous functions[J]. Nonlinear Anal,2007,66(2):498-508.
[12]
Borysenko S D, Ciarletta M, Iovane G. Integro-sum inequalities and motion stability of systems with impulse perturbations[J]. Nonlinear Anal,2005,62(3):417-428.
[13]
Gallo A, Piccirillo A M. About new analogies of Gronwall-Bellman-Bihari type inequalities for discontinuous functions and estimated solution for impulsive differential systems[J]. Nonlinear Anal,2007,67(5):1550-1559.
[14]
Cheung W S. Some new nonlinear inequalities and applications to boundary value problems[J]. Nonlinear Anal,2006,64(9):2112-2128.
[15]
Wang W, Zhou X. A generalized Gronwall-Bellman-Ou-Iang type inequality for discontinuous functions and applications to BVP[J]. Appl Math Comput,2010,216(11):3335-3342.
[16]
Mitropolskiy Y A, Iovane G, Borysenko S D. About a generalization of Bellman-Bihari type inequalities for discontinuous functions and their applications[J]. Nonlinear Anal,2007,66(10):2140-2165.
