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Journal of the London Mathematical Society 2003 67(3):701-714; doi:10.1112/S0024610703004228
© 2003 by London Mathematical Society
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© The London Mathematical Society

Oscillation Criteria for Second-Order Nonlinear Dynamic Equations On Time Scales

Lynn Erbe, Allan Peterson and S. H. Saker

Department of Mathematics and Statistics, University of Nebraska Lincoln, NE 68588-0323, USA lerbe{at}math.unl.edu
Department of Mathematics and Statistics, University of Nebraska Lincoln, NE 68588-0323, USA apeterso{at}math.unl.edu
Faculty of Mathematics and Computer Science, Adam Mickiewicz University Matejki 48/49, 60–769 Poznan, Poland shsaker{at}amu.edu.pl

Received 21 May 2002.

By means of generalized Riccati transformation techniques and generalized exponential functions, some oscillation criteria are given for the nonlinear dynamic equation

Formula
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.

Permanent address: Department of Mathematics, Mansoura University, Mansoura 35516, Egypt


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