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

Meehan, Maria; O’Regan, Donal

Nonlinear Anal., Theory Methods Appl. 31, No. 3-4, 317-341 (1998).

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

Keywords:

existence; integral equations; Volterra equations; fixed point methods; integrodifferential equation; parameter identification; nonlinear delay system; numerical examples

References:

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