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Frequency-domain approach to nonlinear oscillations of some third-order differential equations. (English) Zbl 0612.34050

Generalizing his earlier results [An. Stiint. Univ. Al. I. Cuza Iaşi, N. Ser., Sect. I a 25, 297-302 (1979; Zbl 0426.34044); ibid. 30, 31-34 (1984)] the author uses the frequency-domain matrix inequalities to prove that, under appropriate hypotheses, a third-order differential equation of either of the forms: \[ x\prime''+f(x')x''+g(x')+h(x)=p(t),\quad x\prime''+f(x')x''+g_ 1(x)x'+h(x)=p(t), \] has a solution which, together with its first two derivatives is bounded (respectively, globally exponentially stable, periodic or almost periodic).
Reviewer: S.Mirica

MSC:

34D99 Stability theory for ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations

Citations:

Zbl 0426.34044
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References:

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