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Nonoscillation and asymptotic behaviour for third order nonlinear differential equations

Aydın Tiryaki, A. Okay Çelebi (1998)

Czechoslovak Mathematical Journal

In this paper we consider the equation $y^{'''} + q (t) {y^{'}}^{α} + p (t) h (y) = 0,$ where $p, q$ are real valued continuous functions on $[0, \infty)$ such that $q (t) \geq 0$ , $p (t) \geq 0$ and $h (y)$ is continuous in $(- \infty, \infty)$ such that $h (y) y > 0$ for $y \neq 0$ . We obtain sufficient conditions for solutions of the considered equation to be nonoscillatory. Furthermore, the asymptotic behaviour of these nonoscillatory solutions is studied.

Nonoscillation Criteria for a Class of Nonlinear Differential Equations of Third Order

Cemil Tunc (1997)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

Nonoscillation Criteria for Two-Dimensional Time-Scale Systems

Özkan Öztürk, Elvan Akın (2016)

Nonautonomous Dynamical Systems

We study the existence and nonexistence of nonoscillatory solutions of a two-dimensional systemof first-order dynamic equations on time scales. Our approach is based on the Knaster and Schauder fixed point theorems and some certain integral conditions. Examples are given to illustrate some of our main results.

Nonoscillation Of Nonlinear Retarded Differential Equations

Cheh-Chih Yeh (1979)

Publications de l'Institut Mathématique

Nonoscillation theorems for functional differential equations of arbitrary order.

Graef, John R., Grammatikopoulos, Myron K., Kitamura, Yuichi, Kusano, Takaŝi, Onose, Hiroshi, Spikes, Paul W. (1984)

International Journal of Mathematics and Mathematical Sciences

Nonoscillatory solutions of a second order nonlinear delay differential equation

Ján Ohriska (1985)

Mathematica Slovaca

Nonoscillatory solutions of differential equations with deviating argument

Valter Šeda (1986)

Czechoslovak Mathematical Journal

Nonrectifiable oscillatory solutions of second order linear differential equations

Takanao Kanemitsu, Satoshi Tanaka (2017)

Archivum Mathematicum

The second order linear differential equation ${(p (x) y^{'})}^{'} + q (x) y = 0, x \in (0, x_{0}]$ is considered, where $p$ , $q \in C^{1} (0, x_{0}]$ , $p (x) > 0$ , $q (x) > 0$ for $x \in (0, x_{0}]$ . Sufficient conditions are established for every nontrivial solutions to be nonrectifiable oscillatory near $x = 0$ without the Hartman–Wintner condition.