An Introduction to Difference Equations pp 351-369 | Cite as

# Oscillation Theory

Chapter

## 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.

### Keywords

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### References

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© Springer Science+Business Media New York 1996