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Bounded perturbations with multiple delays of forced harmonic oscillators at resonance. (English) Zbl 0758.34056
The problem of existence of $2\pi$-periodic solutions for the two delay differential equations $x''(t)+x(t)+h\sb 1(x(t-r))+h\sb 2(x(t-s))=p(t)$ 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 {\it R. K. Nagle} and {\it 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.

##### MSC:
 34K99 Functional-differential equations 34C25 Periodic solutions of ODE 34D10 Stability perturbations of ODE 34K10 Boundary value problems for functional-differential equations 34B15 Nonlinear boundary value problems for ODE 34C15 Nonlinear oscillations, coupled oscillators (ODE) 70K30 Nonlinear resonances (general mechanics)