On a Max-Type Difference Equation
© Ali Gelisken et al. 2010
Received: 8 December 2009
Accepted: 23 April 2010
Published: 30 May 2010
Recently, the study of max-type difference equations attracted a considerable attention. Although max-type difference equations are relatively simple in form, it is unfortunately extremely difficult to understand thoroughly the behavior of their solutions; see, for example, [1–20] and the relevant references cited therein. The max operator arises naturally in certain models in automatic control theory (see [13, 14]). Furthermore, difference equation appear naturally as a discrete analogue and as a numerical solution of differential and delay differential equations having applications and various scientific branches, such as in ecology, economy, physics, technics, sociology, and biology.
In this paper, we investigate the asymptotic behavior of the positive solutions of (1.4). We prove that every positive solution of (1.4) converges to Clearly, we can assume that without loss of generality.
2. Main Results
We need the following two lemmas in order to prove the main result of this section.
where initial conditions are real numbers.
We need the following lemma in order to prove the main result of this section.
The authors are grateful to the anonymous referees for their valuable suggestions that improved the quality of this study.
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