On the Fredholm property of linear differential operators with delay and with a small parameter. (Russian) Zbl 0725.34069
Using the small parameter technique, the author establishes some results concerning the stability of the Fredholm property for linear differential operators with retarded argument in integral form when the matrix kernel satisfies Carathéodory-type conditions. A localisation at infinity result for the first order operator equation is also established as a necessary condition for the Fredholm property and a concrete example is exposed.
Reviewer: G.Sebe (St.Martin d’Heres)
MSC:
34K05 | General theory of functional-differential equations |
47G10 | Integral operators |
34K99 | Functional-differential equations (including equations with delayed, advanced or state-dependent argument) |
34A30 | Linear ordinary differential equations and systems |
47E05 | General theory of ordinary differential operators |