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Comparison theorems of Hille-Wintner type for third order linear differential equations

Published online by Cambridge University Press:  17 April 2009

L. Erbe
L. Erbe
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta T6G 2GI, Canada.
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Abstract

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Integral comparison theorems of Hille-Wintner type of second order linear equations are shown to be valid for the third order linear equation y‴ + q(t)y = 0.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 21 , Issue 2 , May 1980 , pp. 175 - 188
Copyright
Copyright © Australian Mathematical Society 1980

References

[1]Barrett, John H., “Oscillation theory of ordinary linear differential equations”, Adv. in Math. 3 (1969), 415–509.CrossRefGoogle Scholar
[2]Erbe, Lynn, “Disconjugacy conditions for the third order linear differential equation”, Canad. Math. Bull. 12 (1969), 603–613.CrossRefGoogle Scholar
[3]Etgen, G.J. and Shih, C.D., “Disconjugacy and oscillation of third order differential equations with nonnegative coefficients”, Proc. Amer. Math. Soc. 38 (1973), 577–582.CrossRefGoogle Scholar
[4]Etgen, G.J. and Shih, C.D., “On the oscillation of certain third order linear differential equations”, Proc. Amer. Math. Soc. 41 (1973), 151–155.CrossRefGoogle Scholar
[5]Etgen, G.J. and Shih, C.D., “Conditions for the nonoscillation of third order differential equations with nonnegative coefficients”, SIAM J. Math. Anal. 6 (1975), 1–8.CrossRefGoogle Scholar
[6]Hallam, Thomas G., “Asymptotic behavior of the solutions of an nth order nonhomogeneous ordinary differential equation”, Trans. Amer. Math. Soc. 122 (1966), 177–194.Google Scholar
[7]Hanan, Maurice, “Oscillation criteria for third-order linear differential equations”, Pacific J. Math. 11 (1961), 919–944.CrossRefGoogle Scholar
[8]Hille, Einar, “Non-oscillation theorems”, Trans. Amer. Math. Soc. 64 (1948), 234–252.CrossRefGoogle Scholar
[9]Jones, Gary D., “Properties of solutions of a class of third-order differential equations”, J. Math. Anal. Appl. 48 (1974), 165–169.CrossRefGoogle Scholar
[10]Jones, Gary D., “An asymptotic property of solutions of y‴ + p′ + qy = 0”, Pacific J. Math. 47 (1973), 135–138.CrossRefGoogle Scholar
[11]Lazer, A.C., “The behavior of solutions of the differential equation y‴ + p(x)y′ + q(x)y = 0”, Pacific J. Math. 17 (1966), 435–466.CrossRefGoogle Scholar
[12]Levin, A.Yu., “A comparison principle for second-order differential equations”, Soviet Math. Dokl. 1 (1960), 1313–1316.Google Scholar
[13]Levin, A.Ju., “Some problems bearing on the oscillation of solutions of linear differential equations”, Soviet Math. Dokl. 4 (1963), 121–124.Google Scholar
[14]Swanson, C.A., Comparison and oscillation theory of linear differential equations (Mathematics in Science and Engineering, 48. Academic Press, New York and London, 1968).CrossRefGoogle Scholar
[15]Wintner, Aurel, “On the comparison theorem of Kneser-Hille”, Math. Scand. 5 (1957), 255–260.CrossRefGoogle Scholar