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The oscillation of a forced equation implies the oscillation of the unforced equation - small forcings. (English) Zbl 0443.34032


MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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[1] Heidel, J. W., Qualitative behaviour of solutions of a third order nonlinear differential equation, Pacific J. Math., 27, 507-526 (1968) · Zbl 0172.11703
[2] Kartsatos, A. G., On \(n\) th-order differential inequalities, J. Math. Anal. Appl., 52, 1-9 (1975) · Zbl 0327.34012
[3] Kartsatos, A. G., \(N\) th order oscillations with middle terms of order \(n-2\), Pacific J. Math., 67, 477-488 (1976) · Zbl 0348.34025
[4] Kartsatos, A. G., Recent results on oscillation of solutions of forced and perturbed nonlinear differential equations of even order, (Graef, J. R., Proceedings, NSF-CBMS Reg. Conference, Stability of Dynamical Systems. Proceedings, NSF-CBMS Reg. Conference, Stability of Dynamical Systems, Mississippi State University (1977), Dekker: Dekker New York) · Zbl 0193.05705
[5] Kiguradge, I. T., Oscillation properties of solutions of certain ordinary differential equations, Soviet Math., 3, 649-652 (1962) · Zbl 0144.11201
[6] Lazer, The behavior of solutions of the differential equation \(y\)″ + \(p(x) y\)′ + \(q(x) y = 0\), Pacific J. Math., 17, 435-465 (1966) · Zbl 0143.31501
[7] Ličko, I.; Švec, M., Le Caractère oscillatoire des solutions de l’équation \(y^{(n)} + f (x) y^{α\) · Zbl 0123.28202
[8] Staikos, V. A.; Sficas, Y. G., Forced oscillations for differential equations of arbitrary order, J. Differential Equations, 17, 1-11 (1975) · Zbl 0325.34082
[9] Wintner, A., A criterion of oscillatory stability, Quart. Appl. Math., 115-117 (1949) · Zbl 0032.34801
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