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Bounded perturbations with multiple delays of forced harmonic oscillators at resonance. (English) Zbl 0758.34056
The problem of existence of 2π-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 R. K. Nagle and 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:
34K99Functional-differential equations
34C25Periodic solutions of ODE
34D10Stability perturbations of ODE
34K10Boundary value problems for functional-differential equations
34B15Nonlinear boundary value problems for ODE
34C15Nonlinear oscillations, coupled oscillators (ODE)
70K30Nonlinear resonances (general mechanics)