Bounded perturbations with multiple delays of forced harmonic oscillators at resonance (Q1199790)

The problem of existence of \(2\pi\)-periodic solutions for the two delay differential equations \(x''(t)+x(t)+h_ 1(x(t-r))+h_ 2(x(t-s))=p(t)\) and \(x''(t)+x(t)+h(x(t-r))+g(x'(t-s)=p(t)\) is investigated. The results which are proved by using a slight modification of an abstract result due to \textit{R. K. Nagle} and \textit{Z. Sinkala} [Differential Equations: Stability and Control, Proc. Int. Conf., Colorado Springs/CO (USA) 1989, Lect. Notes Pure Appl. Math. 127, 401-408 (1990; Zbl 0711.34053)] extend some known results obtained for bounded perturbations of forced harmonic oscillators at resonance and for similar problems where the perturbations involve the derivative of the solution.