×

Bounds for solutions of a nonlinear differential equation of the third order. (English) Zbl 0706.34003

The existence of solutions to the initial value problem for a special nonlinear third order differential equation on the semi-axis is proved. A priori estimates for the solutions, their first derivatives and second quasi-derivatives are found.
Reviewer: S.I.Trofimchuk

MSC:

34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
PDFBibTeX XMLCite
Full Text: EuDML

References:

[1] Филатов А.Н., Шарова Л. В.: Интегральные неравенства и теория нелинейных колебаний. Издательство ”Наука”, Москва 1976. · Zbl 1170.01332
[2] Ráb M.: Bounds for solutions of the equation [p(t)x’]’ + q(t)x = h(t,x,x’). Arch. Math. 2, Scripta Fac. Sci. Nat. UJEP Brunensis, XI, 1975, 79-84.
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.