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Oscillation theorems of nth-order functional differential equations with forcing terms. (English) Zbl 0587.34029
This paper is concerned with the functional differential equations of the form (1) \(x^{(n)}(t)+p(t)x(g(t))=f(t),\) (2) \(x^{(n)}(t)+q(t)x(h(t))=r(t),\) and (3) \(x^{(n)}(t)+p(t)x(g(t))+q(t)x(h(t))=f(t).\) Assuming that some strong conditions hold true, the authors prove that every solution x(t) of (1), (2) and (3) is either oscillatory or else it satisfies: \(\lim_{t\to \infty}x^{(i)}(t)=0\), (0\(\leq i\leq n-1)\).
Reviewer: T.Ding

34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
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[1] Atkinson, F.V, On second-order differential inequalities, (), 109-127 · Zbl 0332.34011
[2] Bradley, J.S, Oscillation theorems for second order delay equations, J. differential equations, 8, 397-403, (1970) · Zbl 0212.12102
[3] Dahiya, R.S, Oscillation and asymptotic behavior of bounded solutions of functional differential equations with delay, J. math. anal. appl., 91, 276-286, (1983) · Zbl 0509.34067
[4] {\scR. S. Dahiya, T. Kusano, and M. Naito}, On almost oscillation of functional differential equations with deviating arguments, J. Math. Anal. Appl., in press. · Zbl 0532.34047
[5] Kiguradze, I.T, On the oscillation of solutions of the equation \(d\^{}\{m\}udt\^{}\{m\} + a(t) ¦u¦\^{}\{n\} sign u = 0\), Mat. sb., 65, 172-187, (1964), (Russian) · Zbl 0135.14302
[6] Onose, H, A comparison theorem and the forced oscillation, Bull. austral. math. soc., 13, 13-19, (1975) · Zbl 0307.34034
[7] Shevelo, B.N, Oscillations of the solutions of differential equations, (1978), Naukova Dumka Press Kiev, (Russian)
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