On periodic solutions of forced second order differential equations with a deviating argument. (English) Zbl 0568.34056

Iannacci, R.; Nkashama, M. N.

Ordinary and partial differential equations, Proc. 8th Conf., Dundee/Scotl. 1984, Lect. Notes Math. 1151, 224-232 (1985).

[For the entire collection see Zbl 0564.00005.]
Using classical Leray-Schauder’s techniques and coincidence degree, we prove the existence of periodic solutions for forced second order delay- differential equations under nonuniform nonresonance conditions with respect to the spectrum of the linear ordinary differential equation with periodicity conditions. Our approach allows us to derive some uniqueness result.

MSC:

34K99	Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34C25	Periodic solutions to ordinary differential equations
34B30	Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)
47H10	Fixed-point theorems
47J05	Equations involving nonlinear operators (general)

Keywords:

Leray-Schauder’s techniques; coincidence degree; forced second order delay-differential equations; nonuniform nonresonance conditions

Citations:

Zbl 0564.00005