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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 \(x''(t)+x(t)+h_ 1(x(t-r))+h_ 2(x(t-s))=p(t)\) 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:

34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34C25 Periodic solutions to ordinary differential equations
34D10 Perturbations of ordinary differential equations
34K10 Boundary value problems for functional-differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
70K30 Nonlinear resonances for nonlinear problems in mechanics

Citations:

Zbl 0711.34053
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