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

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.


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)


Zbl 0564.00005