𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Oscillation of second-order perturbed differential equations

✍ Scribed by Octavian G. Mustafa; Yuri V. Rogovchenko

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
131 KB
Volume
278
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We give constructive proof of the existence of vanishing at infinity oscillatory solutions for a second‐order perturbed nonlinear differential equation. In contrast to most results reported in the literature, we do not require oscillatory character of the associated unperturbed equation, monotonicity of nonlinearity, and we establish global existence of oscillatory solutions without assuming it a priori. Furthermore, as our example demonstrates, existence of bounded oscillatory solutions does not exclude existence of unbounded nonoscillatory solutions. (Β© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

πŸ“œ SIMILAR VOLUMES

Oscillation Criteria for Second Order No
Oscillation Criteria for Second Order Nonlinear Perturbed Differential Equations
✍ Yuri V Rogovchenko πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 263 KB

We present new oscillation criteria for the second order nonlinear perturbed differential equations. These criteria are of a high degree of generality and they extend and unify a number of existing results.

Forced oscillation of second order super
Forced oscillation of second order superlinear differential equations
✍ Yuan Gong Sun; James S. W. Wong πŸ“‚ Article πŸ“… 2005 πŸ› John Wiley and Sons 🌐 English βš– 130 KB

## Abstract In this paper, we establish some new criteria for the oscillation of second order forced nonlinear differential equations (__r__ (__t__ )__x__ β€²(__t__ ))β€² + __p__ (__t__ )__x__ β€²(__t__ ) + __q__ (__t__ )__f__ (__x__ (__t__ )) = __e__ (__t__ ) in both cases when __q__ (__t__ ) < 0 and __

Oscillation of Certain Second-Order Nonl
Oscillation of Certain Second-Order Nonlinear Differential Equations
✍ Wan-Tong Li πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 165 KB

1 Ž Ž .. Ž . where ) 0 is any quotient of odd integers, a g C R, 0, ϱ , q g C R, R , Ž . Ž . Ž . fgC R, R , xf x ) 0, f Ј x G 0 for x / 0. Some new sufficient conditions for Ž . the oscillation of all solutions of ) are obtained. Several examples that dwell upon the importance of our results are als