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On the maintenance of oscillations of \(n\)-th order equations under the effect of a small forcing term. (English) Zbl 0216.11504


MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
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References:

[1] Bhatia, N. P., Some oscillation theorems for second order differential equations, J. Math. Anal. Appl., 15, 442-446 (1966) · Zbl 0144.11104
[2] Bobisud, L. E., Oscillation of nonlinear second order equations, (Proc. Amer. Math. Soc., 23 (1969)), 501-505 · Zbl 0186.41903
[3] Bobisud, L. E., Oscillation of nonlinear differential equations with small nonlinear damping, SIAM J. Appl. Math., 18, 74-76 (1970) · Zbl 0193.05704
[4] Kartsatos, A. G., On oscillations of nonlinear equations of second order, J. Math. Anal. Appl., 24, 665-667 (1968) · Zbl 0203.40003
[5] Kartsatos, A. G., Properties of bounded solutions of nonlinear equations of second order, (Proc. Amer. Math. Soc., 19 (1968)), 1057-1059 · Zbl 0185.16603
[6] Kartsatos, A. G., On oscillation of solutions of even order nonlinear differential equations, J. Differential Equations, 6, 232-237 (1969) · Zbl 0193.05705
[7] Kartsatos, A. G., Contributions to the research of the oscillation and the asymptotic behaviour of solutions of ordinary differential equations, Bull. Soc. Math. Grèce, 10, 1-48 (1969) · Zbl 0202.09601
[8] Kiguradge, I. T., A remark on the oscillation of solutions of the equation \(u′' + a(t) ¦u ¦^nsgnu = 0\), Časopis Pest. Mat., 92, 343-350 (1967), (in Russian)
[9] Legatos, G. G.; Kartsatos, A. G., Further results on the oscillation of solutions of second order equations, Math. Japon., 14, 67-73 (1968) · Zbl 0212.43101
[10] Ryder, G. H.; Wend, D. V.V, Oscillation of solutions of certain ordinary differential equations of \(n\)-th order, (Proc. Amer. Math. Soc., 21 (1970)), 463-469 · Zbl 0201.12102
[11] Švec, M., Monotone solutions of some differential equations, (Colloq. Math., 18 (1967)), 7-21 · Zbl 0153.11002
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