Solutions Of The System Of Maximum Difference Equations

Year 2014, Volume: 2 Issue: 2, 9 - 22, 01.10.2014

Dağıstan Şimşek Ahmet Doğan

Abstract

The behaviour of the solutions of the following system of difference equations is examined.

Keywords

Difference Equation, Maximum Operations, Semicycle

Maksimumlu Fark Denklem Sisteminin Çözümleri

Abstract

Aşağıdaki fark denklem sisteminin çözümlerinin davranışları incelenmiştir.

Keywords

Fark Denklemi, Maksimum Operatörü, Yarı Dönmeler

References

• [1] Amleh A. M., Hoag J. and Ladas G. (1998). A Difference Equation With Eventualy Periodic Solutions, Comput. Math. Appl., 36(10-12), 401-404.
• [2] Janowski, E. J., Kocic, V. L., Ladas, G. and Tzanetopoulos, G., (1998). Global behaviour of solutions of , Journal of Difference Equations and Applications, 3, 297-310.
• [3] Valicenti, S.,(1999). Periodicity and Global Attractivity of Some Difference Equations, University of Rhode Island, (PhD Thesis).
• [4] Teixeria, C. T., (2000). Existence Stability Boundedness and Periodicity of Some Difference Equations, University of Rhode Island, (PhD Thesis).
• [5] Papaschinopoulos, G. and Hatzifilippidis, V., (2001). On a max difference equation, Journal of Mathematical Analysis and Applications, 258, 258-268.
• [6] Mishev D. P. and Patula W. T.,( 2002). A Reciprocal Difference Equation With Maximum, Comput. Math. Appl., 43, 1021-1026.
• [7] Voulov, H. D.,(2002). On the periodic character of some difference equations, Journal of Difference Equations and Applications, 8, 799-810.
• [8] Voulov, H. D.,(2002). Periodic solutions to a difference equation with maximum, Proceedings of the American Mathematical Society, 131, 2155-2160.
• [9] Feuer, J.,( 2003). Periodic solutions of the Lyness max equation, Journal of Mathematical Analysis and Applications, 288, 147-160.
• [10] Papaschinopoulos, G., Schinas, J. and Hatzifilippidis, V.,( 2003). Global behaviour of the solutions of a max-equation and of a system of two max-equation, Journal of Computational Analysis and Applications, 5, 2, 237-247.
• [11] Patula, W. T. and Voulov, H. D.,( 2004). On a max type recursive relation with periodic coefficients, Journal of Difference Equations and Applications, 10, 3, 329-338.
• [12] Cinar C., Stevic S. and Yalcinkaya I. (2005). On The Positive Solutions Of A Reciprocal Difference Equation With Minumum, J. Appl. Math. Computing, 17, 307-314.
• [13] Simsek, D., Cinar, C. and Yalcinkaya, I.,( 2006). On the solution of the difference equation , Int. J. Math. Sci., 1, 10, 481-487.
• [14] Yan, X., Liao, X. and Li, C.,(2006). On a difference equation with maximum, Applied Mathematics and Computation, 181, 1-5.
• [15] Simsek, D., Demir B. and Kurbanlı A.S.,( 2009). x{n+1}=max{1/(x{n},y{n}/x{n}}; y{n+1}=max{1/y{n},x{n}/y{n}} Denklem Sistemlerinin Çözümleri Üzerine, Ahmet Keleşoğlu Eğitim Fakültesi Dergisi, 28, 91-104.
• [16] Simsek D., Demir B. and Cinar C.,( 2009). On the Solutions of the System of Difference Equations x{n+1}=max{A/x{n},y{n}/x{n}}, y{n+1}=max{A/y{n},x{n}/y{n}}, Discrete Dynamics in Nature and Society, Volume 2009, Article ID 325296, 11 pages.
• [17] Simsek D., Kurbanlı A. S., Erdoğan M. E. , ( 2010). x(n+1) = max{1 \ x(n-1) ; y(n-1) \ x(n-1)} ; y(n+1) = max{1 \ y(n-1) ; x(n-1) \ y(n-1)} Fark Denklem Sisteminin Çözümleri, XXIII. Ulusal Matematik Sempozyumu, 153 pp, .04-07 Ağustos 2010, Erciyes Üniversitesi.