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Abstrakty
In the present paper, we investigate the global existence of solutions to initial value problem for nonlinear mixed Volterra-Fredholm functional integrodifferential equations in Banach spaces. The technique used in our analysis is based on an application of the topological transversality theorem known as Leray-Schauder alternative and rely on a priori bounds of solution.
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Czasopismo
Rocznik
Tom
Strony
117--127
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
autor
autor
- Department Of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad-431 004, Maharashtra, India, mbdhakne@yahoo.com
Bibliografia
- [1] T. A. Burton, Volterra integral and differential equations, Academic Press, New York, 1983.
- [2] C. Corduneanu, Integral equations and stability of feedback system, Academic Press, New York, 1973.
- [3] M. B. Dhakne, Global existence of solution of nonlinear functional integral equations, Indian J. Pure Appl. Math. 30(7) (1999), 735–744.
- [4] M. B. Dhakne, S. D. Kendre, On abstract nonlinear mixed Volterra–Fredhom integrodifferential equations, Comm. Appl. Nonlinear Anal. 13(4) (2006), 101–111.
- [5] M. B. Dhakne, H. L. Tidke, On global existence of solution of abstract nonlinear mixed integrodifferential equation with nonlocal condition, Comm. Appl. Nonlinear Anal. 16(1) (2009), 49–59.
- [6] J. Dugundji, A. Granas, Fixed Point Theory, Vol. I, Monografie Matematyczne, PWN Warszawa, 1982.
- [7] W. Fitzgibbon, Semilinear integrodifferential equations in Banach space, Nonlinear Anal. 4 (1980), 745–760.
- [8] J. Hale, Theory of Functional Differential Equations, Springer-Verlag, New York, 1977.
- [9] M. Hussain, On a nonlinear integrodifferential equations in Banach space, Indian J. Pure Appl. Math. 19 (1988), 516–529.
- [10] V. Lakshmikantham, S. Leela, Nonlinear Differential Equations in Abstract Spaces, Pergamon Press, New York, 1981.
- [11] J. Lee, D. O’Regan, Topological transversality, application to initial value problems, Ann. Polon. Math. 48 (1988), 247–252.
- [12] J. Lee, D. O’Regan, Existence results for differential delay equations, J. Differential Equations 102 (1993), 342–359.
- [13] R. MacCamy, An integro-differential equation with applications in heat flow, Quart. Appl. Math. 35 (1977/78), 1–19.
- [14] S. K. Ntouyas, Initial and boundary value problems for functional differential equations via the topological transversality method: A survey, Bull. Greek Math. Soc. 40 (1998), 3–41.
- [15] S. Ntouyas, P. Tsamatos, Inital and boundary value problems for functional differential equations of delay and neutral type, Boll. Un. Mat. Ital. B (7) (1995), 717–734.
- [16] S. Ntouyas, P. Tsamatos, Inital and boundary value problems for functional integrodifferential equations, J. Appl. Math. Stoch. Anal. 7 (1994), 191–201.
- [17] B. G. Pachpatte, Applications of the Leray–Shauder alternative to some Volterra integral and integrodifferential equations, Indian J. Pure. Appl. Math. 26(12) (1995), 1161–1168.
- [18] H. Xia, T. Spanily, Global existence problem for singular functional differential equations, Nonlinear Anal. 20 (1993), 921–934.
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Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA4-0034-0012