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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, USAlerbe@math.unl.edu
ALLAN PETERSON
Affiliation:
Department of Mathematics and Statistics, University of Nebraska, Lincoln, NE 68588-0323, USAapeterso@math.unl.edu
S. H. SAKER
Affiliation:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49, 60–769 Poznan, Polandshsaker@amu.edu.pl Permanent address: Department of Mathematics, Mansoura University, Mansoura 35516, Egypt
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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

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Footnotes

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