Abstract
In this paper we consider positive solutions of the following difference equation
We prove that every positive solution is eventually periodic. Also, we present here some results concerning positive solutions of the difference equation
Similar content being viewed by others
References
A.M. Amleh, J. Hoag and G. Ladas,A difference equation with eventually periodic solutions, Comput. Math. Appl.36 (10–12) (1998), 401–404.
H.M. El-Owaidy, A.M. Ahmed and M.S. Mousa, On asymptotic behaviour of the difference equation\(x_{n + 1} = \alpha + \frac{{x_{n - 1}^p }}{{x_n^p }}\), J. Appl. Math. & Computing12 (1–2) (2003), 31–37.
G. Ladas,Open problems and conjectures, Differ. Equations Appl.2 (1996), 339–341.
G. Ladas,Open problems and conjectures, J. Differ. Equations Appl.4 (3) (1998), 312.
D.P. Mishev and W.T. Patula,A reciprocal Difference Equation with Maximum, Comput. Math. Appl.43 (2002), 1021–1026.
A.D. Mishkis,On some problems of the theory of differential equations with deviating argument, UMN 32:2 (194) (1977), 173–202.
E.P. Popov,Automatic regulation and control, Moscow (1966) (in Russian).
S. Stević, On the recursive sequence\(x_{n + 1} = - \frac{1}{{x_n }} + \frac{A}{{x_{n - 1} }}\), Int. J. Math. Math. Sci.27 (1) (2001), 1–6.
S. Stević, On the recursive sequencex n+1 =g(x n ,x n\t-1)/(A +x n ), Appl. Math. Lett.15 (2002), 305–308.
S. Stević, On the recursive sequencex n+1 =x n\t-1/g(x n ), Taiwanese J. Math.6 (3) (2002), 405–414.
S. Stević, On the recursive sequence\(x_{n + 1} = \frac{{\alpha + \beta x_{n - 1} }}{{1 + g(x_n )}}\), Indian J. Pure Appl. Math.33 (12) (2002), 1767–1774.
S. Stević, On the recursive sequence\(x_{n + 1} = \alpha _n + \frac{{x_{n - 1} }}{{x_n }}\), Dynam. Contin. Discrete Impuls. Systems10a (6) (2003), 911–917.
Z. Zhang, B. Ping and W. Dong,Oscillatory of unstable type second-order neutral difference equations, J. Appl. Math. & Computing9 No. 1 (2002), 87–100.
Z. Zhou, J. Yu and G. Lei,Oscillations for even-order neutral difference equations, J. Appl. Math. & Computing7 No. 3 (2000), 601–610.
Author information
Authors and Affiliations
Corresponding author
Additional information
Stevo Stević received his Ph.D at Belgrade University in 2001. He has written more than 80 original scientific papers and his research interests are mostly in analytic functions of one and several variables, potential theory, difference equations, convergence and divergence of infinite limiting, nonlinear analysis, fixed point theory, operators on function spaces, inequalities and qualitative analysis of differential equations.
Rights and permissions
About this article
Cite this article
Çinar, C., Stević, S. & Yalçinkaya, I. On positive solutions of a reciprocal difference equation with minimum. JAMC 17, 307–314 (2005). https://doi.org/10.1007/BF02936057
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02936057