Some new integral inequalities of Bellman-Bihari type with delay for discontinuous functions

Nonlinear Analysis, Theory, Methods and Applications

Volumn 66, Issue 2, 2007, Pages 498-508

  Iovane, G ^a  

^a UNIVERSITY OF SALERNO   (Italy)

Author keywords

Discontinuous functions; Estimates; Impulsive differential equations; Integral inequalities; Integro sum inequalities; Retardation

Indexed keywords

DIFFERENTIAL EQUATIONS; FUNCTIONS; PARAMETER ESTIMATION; PROBLEM SOLVING;

DISCONTINUOUS FUNCTIONS; ESTIMATES; IMPULSIVE DIFFERENTIAL EQUATIONS; INTEGRAL INEQUALITIES; INTEGRO-SUM INEQUALITIES; RETARDATION;

INTEGRAL EQUATIONS;

EID: 33750979026     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2005.11.043     Document Type: Article

References (32)

1. R.P. Agarwal, Difference Equations and Inequalities: Theory, Method and Applications, New York, 1992
2. Agarwal R.P., and Leela S.G. A brief biography and survey of collected works of V. Lakshmikantham. Lakshmikantham's legacy: a tribute on his 75th birthday. Nonlinear Anal. 40 (2000) 1-19
3. Akinyele O. On Gronwall-Bellman-Bihari-type integral inequalities in several variables with retardation. J. Math. Anal. Appl. 104 1 (1984) 1-26
4. R. Bellman, Theory of solution stability of differential equations, Isdatelstvo Inostz. Lit, Moscow, 1954
5. Bihari J. A generalization of lemma of Bellman and its application to uniqueness problems of differential equations. Acta Math. Acad. Sci. Hung. 7 1 (1956) 71-94
6. Borysenko S.D. Study in solution stability and attraction of the excitation. Kiev (Prepr.) AS Ukr SSR. Inst. Matematiki (1982)
7. Borysenko S.D. About asymptotical stability on linear approximation of the systems with impulse influence. Ukraïn. Mat. Zh. 35 2 (1983) 144-150
8. D.S. Borysenko, About one integral inequality for piece-wise continuous functions, in: Proc. X Int. Kravchuk Conf., Kyiv, 2004, p. 323
9. Borysenko S.D. Construction of Mathematical Models (1995), Vipol, Kiev
10. Borysenko S.D., Iovane G., and Giordano P. Investigations of the properties motion for essential nonlinear. Nonlinear Anal. 62 (2005) 345-363
11. Borysenko S.D., Ciarletta M., and Iovane G. Integro-sum inequalities and motion stability of systems with impulse perturbations. Nonlinear Anal. 62 (2005) 417-428
12. S.D. Borysenko, G. Iovane, P. Giordano, About some hyperbolic impulsive equation and estimates solutions, in: Proc. DE&CAS, Brest, 2005, pp. 9-14
13. G. Iovane, S.D. Borysenko, Boundedness, stability, practical stability of motion Impulsive systems, in: Proc. DE&CAS, Brest, 2005, pp. 15-21
14. Krylov N.N., and Bogolyubov N.N. Introduction in nonlinear mechanics. Izv. Acad. Sci. Ukr. SSR., Kiev (1937)
15. V. Lakshmikantham, Trends in the theory of impulsive differential equations, in: Proc. Internat. Conf. on the Theory and Applications of Differential Equations, Ohio University, 1988, pp. 76-87
16. Lakshmikantham V., Leela S., and Mohan Rao Rama M. Integral and integro-differential inequalities. Appl. Anal. 24 3 (1987) 157-164
17. Lakshmikantham V., and Liu X. Impulsive hybrid systems and stability theory. Dynam. Systems Appl. 7 1 (1998) 1-9
18. Lakshmikantham V., Leela S., and Martynyuk A. Stability analysis of nonlinear systems. Monographs and Textbooks in Pure and Applied Mathematics vol. 125 (1989)
19. Lakshmikantham V., and McRae Farzana A. Basic results for fuzzy impulsive differential equations. Math. Inequal. Appl. 4 2 (2001) 239-246
20. V. Lakshmikantham, Recent trends in the theory of impulsive differential equations, in: Conference of Differential Equations and Applications, Ruse, 1989, 1991, pp. 12-25
21. Lakshmikantham V., Leela S., and Kaul S. Comparison principle for impulsive differential equations with variable times and stability theory. Nonlinear Anal. 22 4 (1994) 499-503
22. Lakshmikantham V., Leela S., and Martynyuk A.A. Practical Stability of Nonlinear Systems (1990), World Scientific Publishing Co.
23. Lakshmikantham V., Bainov D.D., and Simeonov P.S. Theory of impulsive differential equations. Series in Modern Applied Mathematics vol. 6 (1989)
24. Lakshmikantham V. Trends in the theory of impulsive differential equations. Differ. Equ. Appl. 1 (1989) 76-87
25. Lakshmikantham V., and Liu X. On quasistability for impulsive differential systems. Nonlinear Anal. 13 7 (1989) 819-828
26. Lakshmikantham V. Comparison principle for impulsive differential equations with variable times. Comparison Methods and Stability Theory (1993) 227-236
27. Mitropolsky Y.A., Samoilenko A.M., and Perestyuk N. On the problem of substantiation of averaging method for the second order equations with impulse effect. Ukraïn Mat. Zh. 29 6 (1977) 750-762
28. A.M. Samoilenko, S.D. Borysenko, Integro-sum inequalities and stability of processes with discrete disturbances, in: Proc. of Third Int. Conf. "Differential Equations and Applicat.", Bulgaria, 1987, pp. 377-380
29. Samoilenko A.M., and Borysenko S.D. On functional inequalities of Bihari type for discontinuous functions. Uspekhi Mat. Nauk. 53 4 (1998) 147-148
30. Samoilenko A.M., Borysenko S.D., Laserra E., and Matarazzo G. Wendroff type integro-sum inequalities and applications. Math. Notes 3 2 (2002) 123-132
31. Samoilenko A.M., and Perestyuk N.A. Solution stability of differential equations with impulsive excitation. Differ. Uravn. 13 11 (1997) 1981-1992
32. Samoilenko A.M., and Perestyuk N. Differential Equations with Impulse Effect (1987), Visha Shkola, Kyiv