Global behavior of a second order difference equation with two-period coefficient

Authors

  • Ali Yıldırım
  • Durhasan Turgut Tollu Necmettin Erbakan University

Keywords:

Closed form solution, difference equations, global behavior, periodic solution, periodic coefficients.

Abstract

In this paper, we present a detailed study of the following difference equation
x_{n+1}=((α_{n})/(1+x_{n}x_{n-1})), n∈ℕ₀,
where the sequence (α_{n})_{n≥0} is positive, real, periodic with period two and the initial values x₋₁, x₀ are nonnegative real numbers. By this study, we determine global behavior of positive solutions of the above mentioned equation. We also give closed forms of its general solution.

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Published

2021-11-23

Issue

Vol. 16

Section

Vol. 16, No. 4, (2022)

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