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Part of the book series: Undergraduate Texts in Mathematics ((UTM))

Abstract

In previous chapters we were mainly interested in the asymptotic behavior of solutions of difference equations both scalar and nonscalar. In this chapter we will go beyond the question of stability and asymptoticity. Of particular interest is to know whether a solution x(n) oscillates around an equilibrium point x*, regardless of its asymptotic behavior. Since we may assume without loss of generality that x* = 0, the question that we will address here is whether solutions oscillate around zero or whether solutions are eventually positive or eventually negative.

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© 1999 Springer Science+Business Media New York

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Elaydi, S.N. (1999). Oscillation Theory. In: An Introduction to Difference Equations. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3110-1_7

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  • DOI: https://doi.org/10.1007/978-1-4757-3110-1_7

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4757-3112-5

  • Online ISBN: 978-1-4757-3110-1

  • eBook Packages: Springer Book Archive

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