Üstel Biçimdeki Bazı Fark Denklemleri Üzerine

Bu makalede, başlangıç koşulları keyfi pozitif reel sayılar olmak üzere bazı x , , ,,,... x e x x k n 1 n N 012 n k x n n k 1 = n k ! + + + = - - - üstel rasyonel fark denklemlerinin pozitif çözümlerinin lokal asimptotik davranışı araştırılmıştır. Ayrıca, sonuçlarımızı doğrulamak için bazı nümerik örnekler verilmiştir

Anahtar Kelimeler:

Fark denklem, Lokal kararlılık, Pozitif çözümler, Denge noktası

On some difference equations of exponential form

In this paper, the local asymptotic behavior of positive solutions of some exponential difference equations x , , ,,,... x e x x k n 1 n N 012 n k x n n k 1 = n k ! + + + = - - - are investigated where the initial conditions are arbitrary positive real numbers. Furthermore, some numerical examples are presented to verify our results. 2010 AMS-Mathematical Subject Classification Number: 39A10, 39A20

Keywords:

Difference equation, Local stability, Positive solutions, Equilibrium point,

PDF

___

1. Bozkurt, F., 2013. Stability analysis of a nonlinear difference equation. Int. J. Mod. Nonlinear Theory Appl., 2: 1-6.
2. Camouzis, E., Ladas, G. 2007. Dynamics of third-order rational difference equations with open problems and conjectures, CRC Press.
3. Elaydi, S., 1996. An introduction to difference equation, New York, Springer.
4. El-Metwally, H., Grove, E. A., Ladas, G., Levins, R., Radin, M. 2011. On the difference equation, Nonlinear Anal., 47, 4623-4634.
5. Gocen, M., Guneysu, M., 2018. The global attractivity of some rational difference equations. J. Comput. An. App., 25(7): 1233-1243.
6. Gumus, M., Abo-Zeid R. 2018. On the solutions of a (2k+2) th order difference equation. Dyn. Contin., Disc. Imp. Sys. Ser. B, 25: 129-143.
7. Gumus, M. 2018. The global asymptotic stability of a system of difference equations. J. Diff. Eq. App., 24(6):976-991. doi. org/10.1080/10236198.2018.1443445.
8. Kocić, V., Ladas, G. 1993. Global behavior of nonlinear difference equations of higher order with applications, Kluwer Academic Publishers, Dordrecht.
9. Kulenović, M. R. S., Ladas, G. 2001. Dynamics of second order rational difference equations, Chapman & Hall/CRC. 10. Okumus, I., Soykan, Y., 2018. Some Technique To Show The Boundedness Of Rational Difference Equations, Journal of Progressive Research in Mathematics, 13(2), 2246-2258.
11. Ozturk, I., Bozkurt, F., Ozen, S. 2006. On the difference equation , Appl. Math. Comput., 181, 1387-1393.
12. Tasdemir, E., Soykan, Y., 2017. Long-term behavior of solutions of the non-linear difference equation, 1. Gen. Math. Not., 38(1): 13-31.