×

Existence theory for nonlinear Volterra integrodifferential and integral equations. (English) Zbl 0891.45004

The authors study parameter identification problems for the nonlinear delay system with state dependent delays \[ x'(t)= f\Biggl(t,x(t), \int^0_{-r} d_s\mu(s,t,x_t,\sigma) x(t+ s),\theta\Biggr), \] where \(0\leq t\leq T\), and \(x(t)= \phi(t)\), \(-r\leq t\leq 0\). Under assumptions, too complicated to be stated here, an identification method is outlined. Some numerical examples are given.
Reviewer: S.O.Londen (Espoo)

MSC:

45J05 Integro-ordinary differential equations
45G10 Other nonlinear integral equations
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Lee, J. W. and O’Regan, D., Existence principles for nonlinear integral equations on semiinfinite and half-open intervals. Advances in Nonlinear Dynamics. Gordon & Breach. (To appear.)
[2] Gripenberg, G.; Londen, S.O.; Staffans, O., Volterra integral and functional equations, (1990), Cambridge University Press New York · Zbl 0695.45002
[3] Nohel, J.A.; Shea, D.F., Frequency domain methods for Volterra equations, Adv. math., 22, 278-304, (1976) · Zbl 0349.45004
[4] Brezis, H.; Browder, F.E., Existence theorems for nonlinear integral equations of Hammerstein type, Bull. amer. math. soc., 81, 73-78, (1975) · Zbl 0298.47031
[5] O’Regan, D., Existence theory for nonlinear Volterra and Hammerstein integral equations, (), 601-615, World Scientific Series in Applicable Analysis, River Edge, New Jersey · Zbl 0842.45003
[6] O’Regan, D., Existence results for nonlinear integral equations, J. math. anal. appl., 192, 705-726, (1995) · Zbl 0851.45003
[7] Pachpatte, B.G., 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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.