On some generalizations Bellman-Bihari result for integro-functional inequalities for discontinuous functions and their applications

Boundary Value Problems

Volumn 2009, Issue , 2009, Pages

  Gallo, Angela ^a   Piccirillo, Anna Maria ^b  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

^b SECOND UNIVERSITY OF NAPLES   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70349739322     PISSN: 16872762     EISSN: 16872770     Source Type: Journal    
DOI: 10.1155/2009/808124     Document Type: Article

References (23)

1. D. Banov and P. Simeonov, Integral Inequalities and Applications, vol. 57 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1992.
2. S. D. Borysenko, G. Iovane, and P. Giordano, "Investigations of the properties motion for essential nonlinear systems perturbed by impulses on some hypersurfaces," Nonlinear Analysis: Theory, Methods & Applications, vol. 62, no. 2, pp. 345-363, 2005.
3. S. D. Borysenko, M. Ciarletta, and G. Iovane, "Integro-sum inequalities and motion stability of systems with impulse perturbations," Nonlinear Analysis: Theory, Methods & Applications, vol. 62, no. 3, pp. 417-428, 2005.
4. S. Borysenko and G. Iovane, "About some new integral inequalities of Wendroff type for discontinuous functions," Nonlinear Analysis: Theory, Methods & Applications, vol. 66, no. 10, pp. 2190-2203, 2007.
5. S. C. Hu, V. Lakshmikantham, and S. Leela, "Impulsive differential systems and the pulse phenomena," Journal of Mathematical Analysis and Applications, vol. 137, no. 2, pp. 605-612, 1989.
6. V. Lakshmikantham and S. Leela, Differential and Integral Inequalities, Theory and Applications, Academic Press, New York, NY, USA, 1969.
7. V. Lakshmikantham, S. Leela, and M. Mohan Rao Rama, "Integral and integro-differential inequalities," Applicable Analysis, vol. 24, no. 3, pp. 157-164, 1987.
8. V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6 of Series in Modern Applied Mathematics, World Scientific, Teaneck, NJ, USA, 1989.
9. A. A. Martyhyuk, V. Lakshmikantham, and S. Leela, Stability of Motion: the Method of Integral Inequalities, Naukova Dumka, Kyiv, Russia, 1989.
10. Yu. A. Mitropolskiy, S. Leela, and A. A. Martynyuk, "Some trends in V. Lakshmikantham's investigations in the theory of differential equations and their applications," Differentsial'nye Uravneniya, vol. 22, no. 4, pp. 555-572, 1986.
11. Yu. A. Mitropolskiy, A. M. Samoilenko, and N. Perestyuk, "On the problem of substantiation of overoging method for the second equations with impulse effect," Ukrainskii Matematicheskii Zhurnal, vol. 29, no. 6, pp. 750-762, 1977.
12. Yu. A. Mitropolskiy, G. Iovane, and S. D. Borysenko, "About a generalization of Bellman-Bihari type inequalities for discontinuous functions and their applications," Nonlinear Analysis: Theory, Methods & Applications, vol. 66, no. 10, pp. 2140-2165, 2007.
13. A. M. Samoilenko and N. Perestyuk, Differential Equations with Impulse Effect, Visha Shkola, Kyiv, Russia, 1987.
14. A. Gallo and A. M. Piccirillo, "About new analogies of Gronwall-Bellman-Bihari type inequalities for discontinuous functions and estimated solutions for impulsive differential systems," Nonlinear Analysis: Theory, Methods & Applications, vol. 67, no. 5, pp. 1550-1559, 2007.
15. J. J. Nieto, "Impulsive resonance periodic problems of first order," Applied Mathematics Letters, vol. 15, no. 4, pp. 489-493, 2002.
16. J. J. Nieto, "Basic theory for nonresonance impulsive periodic problems of first order," Journal of Mathematical Analysis and Applications, vol. 205, no. 2, pp. 423-433, 1997.
17. J. J. Nieto, "Periodic boundary value problems for first-order impulsive ordinary differential equations," Nonlinear Analysis: Theory, Methods & Applications, vol. 51, no. 7, pp. 1223-1232, 2002.
18. Z. Luo and J. J. Nieto, "New results for the periodic boundary value problem for impulsive integro-differential equations," Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 6, pp. 2248-2260, 2009.
19. J. J. Nieto and D. O'Regan, "Variational approach to impulsive differential equations," Nonlinear Analysis: Real World Applications, vol. 10, no. 2, pp. 680-690, 2009.
20. M. Benchohra, J. Henderson, and S. Ntouyas, Impulsive Differential Equations and Inclusions, vol. 2 of Contemporary Mathematics and Its Applications, Hindawi Publishing Corporation, New York, NY, USA, 2006.
21. G. Iovane, "Some new integral inequalities of Bellman-Bihari type with delay for discontinuous functions," Nonlinear Analysis: Theory, Methods & Applications, vol. 66, no. 2, pp. 498-508, 2007.
22. A. Samoilenko, S. Borysenko, C. Cattani, G. Matarazzo, and V. Yasinsky, Differential Models: Stability, Inequalities and Estimates, Naukova Dumka, Kiev, Russia, 2001.
23. D. S. Borysenko, A. Gallo, and R. Toscano, "Integral inequalities Gronwall-Bellman type for discontinuous functions and estimates of solutions impulsive systems," in Proc.DE@CAS, pp. 5-9, Brest, 2005.