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Boundedness and oscillation for nonlinear dynamic equations on a time scale


Authors: Lynn Erbe and Allan Peterson
Journal: Proc. Amer. Math. Soc. 132 (2004), 735-744
MSC (2000): Primary 39A10
Published electronically: July 14, 2003
MathSciNet review: 2019950
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Abstract | References | Similar Articles | Additional Information

Abstract: We obtain some boundedness and oscillation criteria for solutions to the nonlinear dynamic equation

\begin{displaymath}(p(t)x^{\Delta }(t))^{\Delta }+q(t)(f\circ x^{\sigma })=0, \end{displaymath}

on time scales. In particular, no explicit sign assumptions are made with respect to the coefficient $q(t)$. We illustrate the results by several examples, including a nonlinear Emden-Fowler dynamic equation.


References [Enhancements On Off] (What's this?)

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Additional Information

Lynn Erbe
Affiliation: Department of Mathematics and Statistics, University of Nebraska-Lincoln, Lincoln, Nebraska 68588-0323
Email: lerbe@math.unl.edu

Allan Peterson
Affiliation: Department of Mathematics and Statistics, University of Nebraska-Lincoln, Lincoln, Nebraska 68588-0323
Email: apeterso@math.unl.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07061-8
Received by editor(s): June 27, 2002
Received by editor(s) in revised form: October 21, 2002
Published electronically: July 14, 2003
Additional Notes: This research was supported by NSF Grant 0072505
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2003 American Mathematical Society