×

zbMATH — the first resource for mathematics

On an asymptotic behaviour of solutions of the differential equation of the fourth order. (English) Zbl 0595.34053
Consider the fourth order linear differential equation \[ (*)\quad y^{(iv)}+p(t)y''+q(t)y'-(-1)^ mr(t)y=0,\quad m=1,2, \] where p,q,r are continuously differentiable functions and \(r(t)>0\) on [a,\(\infty)\). The author discusses asymptotic formulae of the first canonical form relative to (*).
Reviewer: V.Lakshmikantham

MSC:
34D05 Asymptotic properties of solutions to ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34A30 Linear ordinary differential equations and systems
PDF BibTeX XML Cite
Full Text: EuDML
References:
[1] CODDINGTON E. A., LEVINSON N.: Theory of Ordinary Differential Equations. New York 1955. · Zbl 0064.33002
[2] HINTON D. B.: Asymptotic behaviour of solutions of (ry(m))(k)\pm qy=0. J. Differential Equations, 4, 1968, 590-596. · Zbl 0175.38101
[3] HUSTÝ Z.: Asymptotické vlastnosti integrálů homogenní lineární diferenciální rovnice čtvrtého řádu. Časopis pro pěstování matematik,y roč. 83 1958, Praha, str. 60-69.
[4] HUSTÝ Z.: O některých vlastnostech homogenní lineární diferenciální rovnice čtvrtého řádu. Časopis pro pěstování matematiky, roč. 83 1958, Praha, str. 202-213.
[5] MAMRILLA J.: O niektorých vlastnostiach riešení lineárnej diferenciálnej rovnice y(iv) + 2A(x)y’ +(A’(x) + B(x))y = 0. Acta Fac. RN Univ. Comen, X, 3, Mathematica, 12, 1965.
[6] MAMRILLA J.: Bemerkung zur Oscillationsfähigheit der Losungen der Gleichung y(iv) + A(x)y’ + B(x)y = 0. Acta Fac. R. N. Univ. Comen. - Mathematica 31, 1975. · Zbl 0309.34027
[7] PFEIFER G. W.: Asymptotic solutions of the equation y”’ + qy’ + ry = 0. Differential Equations, 11, 1972, 145-155. · Zbl 0263.34057
[8] ROVDER J.: Asymptotic behaviour of solutions of the differential equation of the fourth order. Math. Slovaca 30, 1980, 379-392. · Zbl 0482.34050
[9] ROVDER J.: Oscillatory Properties of the fourth order linear differential equation. Math. Slovaca 33, 1983, 371-379. · Zbl 0525.34027
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.