×

Asymptotic property of solutions of a class of third-order differential equations. (English) Zbl 0721.34025

The authors study asymptotic properties of solutions of \((1)\quad y'''+a(t)y''+b(t)y'+c(t)y=0\) and obtain some sufficient conditions so that (1) admits an oscillatory solution.

MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34C11 Growth and boundedness of solutions to ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] L. Erbe, Existence of oscillatory solutions and asymptotic behavior for a class of third order linear differential equations, Pacific J. Math. 64 (1976), no. 2, 369 – 385. · Zbl 0339.34030
[2] Maurice Hanan, Oscillation criteria for third-order linear differential equations., Pacific J. Math. 11 (1961), 919 – 944. · Zbl 0104.30901
[3] Gary D. Jones, An asymptotic property of solutions of \?”’+\?\?\(^{\prime}\)+\?\?=0, Pacific J. Math. 47 (1973), 135 – 138. · Zbl 0264.34040
[4] Gary D. Jones, Oscillatory behavior of third order differential equations, Proc. Amer. Math. Soc. 43 (1974), 133 – 136. · Zbl 0259.34039
[5] A. C. Lazer, The behavior of solutions of the differential equation \?”’+\?(\?)\?\(^{\prime}\)+\?(\?)\?=0, Pacific J. Math. 17 (1966), 435 – 466. · Zbl 0143.31501
[6] C. A. Swanson, Comparison and oscillation theory of linear differential equations, Academic Press, New York-London, 1968. Mathematics in Science and Engineering, Vol. 48. · Zbl 0191.09904
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.