Second order Volterra-Fredholm functional integrodifferential equations
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DOI:
https://doi.org/10.26637/mjm0101/001Abstract
This paper deals with the study of global existence of solutions to initial value problem for second order 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 .
Keywords:
Global solution, Volterra-Fredholm functional integrodifferential equation, Leray-Schauder alternative, Fixed point, Priori boundsMathematics Subject Classification:
47H10, 35R10- Pages: 1-7
- Date Published: 01-09-2012
- Vol. 1 No. 1 (2012): Inaugural Issue :: Malaya Journal of Matematik (MJM)
T. A. Burton, Volterra integral and differential equations, Academic Press, New York, 1983.
M. B. Dhakne, S. D. Kendre, On abstrct nonlinear mixed Volterra- Fredhom integrodifferential equations, Communications on Applied Nonlinear Analysis, 13(4) (2006), 101-111. DOI: https://doi.org/10.7153/mia-09-64
M. B. Dhakne, G. B. Lambh, On an abstrct nonlinear second order integrodifferential equation, Journal of Function Space and Application, 5(2) (2007), 167-174. DOI: https://doi.org/10.1155/2007/654745
M. B. Dhakne, H. L. Tidke, On global existance of solution of abstrct nonlinear mixed integrodifferential equation with nonlocal condition, Communications on Applied Nonlinear Analysis, 16(1)(2009), 49-59.
J. Dugundji, A. Granas, Fixed Point Theory, Vol. I, Monographie Matematycane, PNW Warsawa, 1982.
W. Fitzgibbon, Semilinear integrodifferential equations in Banach space, Nonlinear Analysis, 4(1980), 745-760. DOI: https://doi.org/10.1016/0362-546X(80)90075-9
J. Hale, Theory of Functinal Differential Equations, Springer-Verlag, New York, 1977. DOI: https://doi.org/10.1007/978-1-4612-9892-2
M. Hussain, On a nonlinear integrodifferential equations in Banach space, Indian J. Pure Appl. Math., 19(1988), 516-529.
V. Lakshmikantham, S. Leela, Nonlinear Differential Dquations in Abstract Spaces, Pergamon Press, New York, 1981.
J. Lee, D. O’Regon, Topological transversality, application to initial value problems, Ann. Pol. Math., 48(1988), 247-252. DOI: https://doi.org/10.4064/ap-48-3-247-252
J. Lee, D. O’Regon, Existance results for differential delay equations, Inter. Journal. Differential Equations, 102(1993), 342-359. DOI: https://doi.org/10.1006/jdeq.1993.1033
R. MacCamy, An integro-differential equation with applications in heat flow, Quart. Appl. Math., 35(1977/78), 1-19. DOI: https://doi.org/10.1090/qam/452184
S. K. Ntouyas,Global existance for volterra functional integro-differential equations, Panam. Math. J., 8(1998), 37-43.
S. K. Ntouyas, Initial and boundary value problems for functional differential equations via the topological transversality method, Bull. Greek Math. Soc., 40 (1998), 3-41.
S. K. Ntouyas, Y. Sficas, P. Tsamatos, An existance principle for boundary value problems for second order functinal integro-differential equations, Nonlinear Analysis, 20(1993), 215-222. DOI: https://doi.org/10.1016/0362-546X(93)90159-P
S. K. Ntouyas, P. Tsamatos, Inital and boundary value problems for functinal Integro-differential equations, J. Appl. Math. Stoch. Analysis, 7(1994), 191-201. DOI: https://doi.org/10.1155/S1048953394000195
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.
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