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Öğe Beşinci mertebeden fark denklem sisteminin çözülebilirliği üzerine(Eskişehir Teknik Üniversitesi, 2019) Yazlık, Yasin; Kara, MerveSon zamanlarda lineer olmayan fark denklemeleri ve bu denklemlerin sistemleri ile ilgili literatürde çok fazla sayıda çalışma vardır [1-36]. Lineer olmayan fark denklemleri ya da fark denklem sistemlerinin dikkat çeken bir yönü de kapalı ya da açık formda çözülebilen denklem ya da sistemler bulabilmektir. Bu tipteki fark denklemlerinin ya da onların sistemlerinin çözümleri için elde edilen formüller, denklemlerin ya da onların sistemlerinin çözümlerinin bir çok özelliğini belirlemede kullanılabileceği açıktır. Bu nedenle lineer olmayan bir fark denklemi veya sisteminin çözümlerini elde etmek ilgi çekici olmasının yanında oldukça önemlidir.Öğe Global behavior of two-dimensional difference equations system with two period coefficients(Tbilisi Center for Mathematical Sciences, 2020) Kara, Merve; Tollu, Durhasan Turgut; Yazlık, YasinIn this paper, we investigate the following system of difference equations x(n+1) = alpha(n)/1 + y(n)x(n-1), y(n+1) = beta(n)/1 + x(n)y(n-1), n is an element of N-0, where the sequences (alpha(n))(n is an element of N0), (beta(n))(n is an element of N0) are positive, real and periodic with period two and the initial values x(-1), x(0), y(-1), y(0) are non-negative real numbers. We show that every positive solution of the system is bounded and examine their global behaviors. In addition, we give closed forms of the general solutions of the system by using the change of variables. Finally, we present a numerical example to support our results.Öğe On a solvable system of difference equations of higher-order with period two coefficıents(Ankara University, 2019) Yazlık, Yasin; Kara, MerveWe show that the next di§erence equations system xn+1 = anxnk+1ynk yn n + n+1; yn+1 = bnynk+1xnk xn n + n+1; n 2 N0; where N0 = N [ f0g, the sequences (an)n2N0 , (bn)n2N0 , ( n)n2N0 , (n)n2N0 are two periodic and the initial conditions xi, yi i 2 f0; 1; : : : ; kg, are nonzero real numbers, can be solved. Also, we investigate the behavior of solutions of above mentioned system when a0 = b1 and a1=ba.Öğe On a solvable three-dimensional system of difference equations(University of Nis, 2020) Kara, Merve; Yazlık, Yasinn this paper, we show that the following three-dimensional system of difference equations (Formula Presented) where the parameters a, b, c, d, e, f and the initial values x?i, y?i, z?i, i ? {1, 2, 3}, are real numbers, can be solved, extending further some results in literature. Also, we determine the asymptotic behavior of solutions and the forbidden set of the initial values by using the obtained formulas.Öğe On a three dimensional higher order system of difference equations(Watam Press, 2022) Akrour, Youssouf; Kara, Merve; Touafek, Nouressadat; Yazlık, YasinIn this work, we derive the solutions form of the following three-dimensional system of nonlinear difference equations of higher-order (Formula presented). where the parameters ?, ?, a, b, A, B and the initial values x?i, y?i, z?i, i ? {0, 1, …, k} are non-zero real numbers. provided in details. The behavior of the solutions of our system with p = 1 is.Öğe Solvability of a system of higher order nonlinear difference equations(Hacettepe University, 2020) Kara, Merve; Yazlık, Yasin; Tollu, Durhasan TurgutIn this paper we show that the system of difference equations xn = ayn-k + dyn-kxn-(k+l)/bxn-(k+l) + cyn-l, yn = ?xn-k + ?xn-kyn-(k+l)/?yn-(k+l) + ?xn-l, where n ? ?0, k and l are positive integers, the parameters a, b, c, d, ?, ?, ?, ? are real numbers and the initial values x-j, y-j, j = 1, k + l, are real numbers, can be solved in the closed form. We also determine the asymptotic behavior of solutions for the case l = 1 and describe the forbidden set of the initial values using the obtained formulas. Our obtained results significantly extend and develop some recent results in the literature.Öğe Solvability of a system of nonlinear difference equations of higher order(TUBITAK, 2019) Kara, Merve; Yazlık, YasinIn this paper, we show that the following higher-order system of nonlinear difference equations, xn=xn-kyn-k-l/yn-l(an+bnxn-kyn-k-l, yn=yn-kxn-k-l/xn-l(?n+ßnyn-kxn-k-l), n?0, where k, l,? , (an)n ? 0, (bn)n ? 0, (?n)n ? 0, (ßn)n ? 0 and the initial values x-i; y-i, i = 1, k + l , are real numbers, can be solved and some results in the literature can be extended further. Also, by using these obtained formulas, we investigate the asymptotic behavior of well-defined solutions of the above difference equations system for the case k = 2, l = k. © Tübitak.Öğe Well-defined solutions of a three-dimensional system of difference equations(Gazi University, 2020) Kara, Merve; Touafek, Nouressadat; Yazlık, YasinWe show that the three-dimensional system of difference equations [ Formula Presented] n ? N0, where the parameters a, b, c, ?, ?, ? and the initial conditions x?i, y?i, z?i, i ? {0,1}, are non-zero real numbers, can be solved. Using the obtained formulas, we determine the asymptotic behavior of solutions and give conditions for which periodic solutions exist. Some numerical examples are given to demonstrate the theoretical results.
