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A second-order half-linear ordinary differential equation of the type $(| y^{'} |^{α - 1} y^{'})^{'} + α q (t) {| y |}^{α - 1} y = 0 (1)$ is considered on an unbounded interval. A simple oscillation condition for (1) is given in such a way that an explicit asymptotic formula for the distribution of zeros of its solutions can also be established.

Analytic results for oscillatory systems with extremal dynamic properties

Henryk Górecki, Mieczysław Zaczyk (2014)

International Journal of Applied Mathematics and Computer Science

Another proof of Borůvka's criterion on global equivalence of the second order ordinary linear differential equations

František Neuman (1990)

Časopis pro pěstování matematiky

Approximate methods for calculating the period of oscillations for the generalized Lienard's differential equation

Eid, M.H., Anwar, M.N., El-Serafi, S.A. (1982)

Portugaliae mathematica

Approximation in Lie transformation groups by superposition of one-parameter subgroups. (Approximation in Lieschen Transformationsgruppen durch Überlagerung von einparametrigen Untergruppen.)

Wallner, Johannes (1995)

Mathematica Pannonica

Asymptotic analyses of two fourth order linear differential equations

David Lowell Lovelady (1980)

Annales Polonici Mathematici

Asymptotic analysis of $n$ -th order differential equations

Jozef Džurina (1997)

Mathematica Slovaca

Asymptotic and oscillation properties of third order linear differential equations

Drahoslava Radochová, Václav Tryhuk (1980)

Archivum Mathematicum

Asymptotic and oscillatory behavior of solutions of differential equations with advanced arguments

Olusola Akinyele, Rajbir S. Dahiya (1990)

Archivum Mathematicum

Asymptotic and oscillatory behaviour of solutions of certain second order neutral differential equations with forcing term

Staněk, Svatoslav (1992)

Mathematica Slovaca

Asymptotic behavior of non-linear inhomogeneous differential equations via non-standard analysis. Part II. Some applications to higher order equations

Vadím Komkov (1974)

Annales Polonici Mathematici

Asymptotic behavior of non-linear inhomogeneous equations via non-standard analysis. Part I. Second order equations

Vadim Komkov, Carter Waid (1973)

Annales Polonici Mathematici

Asymptotic behavior of solutions of a $2 n^{t h}$ order nonlinear differential equation

C. S. Lin (2002)

Czechoslovak Mathematical Journal

In this paper we prove two results. The first is an extension of the result of G. D. Jones [4]: (A) Every nontrivial solution for $\}\begin{matrix} {(- 1)}^{n} u^{(2 n)} + f (t, u) = 0, in (α, \infty), u^{(i)} (ξ) = 0, i = 0, 1, \dots, n - 1, and ξ \in (α, \infty), \end{matrix}$ must be unbounded, provided $f (t, z) z \geq 0$ , in $E \times ℝ$ and for every bounded subset $I$ , $f (t, z)$ is bounded in $E \times I$ . (B) Every bounded solution for ${(- 1)}^{n} u^{(2 n)} + f (t, u) = 0$ , in $ℝ$ , must be constant, provided $f (t, z) z \geq 0$ in $ℝ \times ℝ$ and for every bounded subset $I$ , $f (t, z)$ is bounded in $ℝ \times I$ .

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