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Global existence for neutral functional integrodifferential equations. (English) Zbl 0890.45004

The author considers the existence of a solution in a compact interval for the initial value problem for a class of nonlinear first order functional differential equations of neutral type. The same is studied for the initial value problem for a second order equation. The results are obtained by a direct application of the Schauder fixed point theorem.

MSC:

45J05 Integro-ordinary differential equations
45G10 Other nonlinear integral equations
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References:

[1] Hale, J., Theory of Functional Differential Equations (1977), Springer-Verlag
[2] Ntouyas, S.; Sficas, Y.; Tsamatos, P., Existence results for initial value problems for neutral functional differential equations, J. Differential Equations, 114, 527-537 (1994) · Zbl 0810.34061
[3] Ntouyas, S.; Tsamatos, P., Global existence for functional integro-differential equations of delay and neutral type, Applicable Analysis, 54, 251-262 (1994) · Zbl 0838.34078
[4] Ntouyas, S.; Tsamatos, P., Initial and boundary value problems for functional integro-differential equations, J. Appl. Math. Stock. Analysis, 7, 191-201 (1994) · Zbl 0804.34058
[5] Pachpatte, B., Applications of the Leray-Schauder Alternative to some Volterra integral and integrodifferential equations, Indian J. pure appl. Math., 26, 1161-1168 (1995) · Zbl 0852.45012
[6] Dugundji, J.; Granas, A., Fixed Point Theory, (Monographie Matematyczne, Vol. I (1982), PNW Warsawa: PNW Warsawa New York) · Zbl 1025.47002
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