Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-26T14:58:08.823Z Has data issue: false hasContentIssue false
  • English
  • Français

OSCILLATION CRITERIA FOR SECOND-ORDER NONLINEAR DYNAMIC EQUATIONS ON TIME SCALES

Published online by Cambridge University Press:  20 May 2003

LYNN ERBE ,
ALLAN PETERSON  and
S. H. SAKER
LYNN ERBE
Affiliation:
Department of Mathematics and Statistics, University of Nebraska, Lincoln, NE 68588-0323, [email protected]
ALLAN PETERSON
Affiliation:
Department of Mathematics and Statistics, University of Nebraska, Lincoln, NE 68588-0323, [email protected]
S. H. SAKER
Affiliation:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49, 60–769 Poznan, [email protected] Permanent address: Department of Mathematics, Mansoura University, Mansoura 35516, Egypt
Get access

Abstract

By means of generalized Riccati transformation techniques and generalized exponential functions, some oscillation criteria are given for the nonlinear dynamic equation \[ (p(t)x^{\Delta} (t))^{\Delta}+q(t)(f\circ x^{\sigma})=0 \] on time scales. The results are also applied to linear and nonlinear dynamic equations with damping, and some sufficient conditions are obtained for the oscillation of all solutions.

Keywords

34K1139A1039A9934C1039A11
Type
Research Article
Information
Journal of the London Mathematical Society , Volume 67 , Issue 3 , June 2003 , pp. 701 - 714
Copyright
The London Mathematical Society 2003

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

The research described in this paper was supported by NSF grant 0072505.