共查询到20条相似文献，搜索用时 15 毫秒
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Stevo Stevi&#x; Durhasan T. Tollu 《Mathematical Methods in the Applied Sciences》2019,42(10):3579-3615
An analysis of semi‐cycles of positive solutions to eight systems of difference equations of the following form where a ∈ [0, + ∞), the sequences pn, qn, rn, sn are some of the sequences xn and yn, with positive initial values x?j,y?j, j = 1,2, is conducted in detail, and it is shown that these systems can be solved in closed‐form, which is the main result here. Two methods for showing the solvability are described. 相似文献
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Stevo Stevi&#x; Durhasan T. Tollu 《Mathematical Methods in the Applied Sciences》2019,42(12):4065-4112
We have studied recently solvability and semi‐cycles of eight systems of difference equations of the following form: where a ∈ [0, + ∞), the sequences pn, qn, rn, sn are some of the sequences xn and yn, with positive initial values x?j,y?j, j = 1,2, in detail. This paper is devoted to the study of the other eight systems of the form. We show that these systems are also solvable in closed form and describe semi‐cycles of their solutions complementing our previous results on such systems of difference equations. 相似文献
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Stevo Stević 《Mathematical Methods in the Applied Sciences》2020,43(3):1001-1016
We show that the following nonlinear system of difference equations where parameters a,b,c,d and initial values x−1,x0,y−1,y0 are real numbers, is solvable in closed form, considerably generalizing some recent results. To do this, we use the method of transformation along with several tricks, transforming the system to some known solvable difference equations, by use of which we obtain some closed-form formulas for general solution to the system. The following five cases are considered separately: (1) c=0; (2) d=0; (3) a=0; (4) b=0; and (5) abcd≠0. 相似文献
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Stevo Stevi&#x; Bratislav Iri
anin Witold Kosmala 《Mathematical Methods in the Applied Sciences》2019,42(9):2974-2992
We present a natural method for solving the difference equation where , parameter a, and initial values x?j, , , are real or complex numbers. As a concrete example, the case k = 1, l = 2 is studied in detail, and several interesting formulas for solutions and objects used in the analysis of the equation are given. A useful remark on solvability of difference equations on complex domains is presented and used here. 相似文献
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Mohamed M. El‐Dessoky 《Mathematical Methods in the Applied Sciences》2016,39(5):1076-1092
In this paper, we deal with the system that has solutions and the periodicity character of the following systems of rational difference equations with order three with initial conditions x?2,x?1,x0,y?2,y?1, and y0 that are arbitrary nonzero real numbers. Some numerical examples will be given to illustrate our results. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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常系数齐次线性差分方程组的求解方法,已有作者讨论过,但都没有给出一个比较简便的计算方法.本文将给出一个十分简明而有效的常系数齐次线性差分方程组的新求解方法. 相似文献
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Tarek F. Ibrahim Nouressadat Touafek 《Mathematical Methods in the Applied Sciences》2014,37(16):2562-2569
This paper deals with the form and the periodicity of the solutions of the max‐type system of difference equations where , and are positive two‐periodic sequences and initial values x0, x ? 1, y0, y ? 1 ∈ (0, + ∞ ). Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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We investigate in this paper the solutions and the periodicity of the following rational systems of difference equations of three‐dimensional with initial conditions x?2,x?1,x0,y?2,y?1,y0,z?2,z?1andz0 are nonzero real numbers. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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Nabila Haddad Nouressadat Touafek Julius Fergy T. Rabago 《Mathematical Methods in the Applied Sciences》2017,40(10):3599-3607
The solution form of the system of nonlinear difference equations where the coefficients a ,b ,α ,β and the initial values x ? i ,y ? i ,i ∈{0,1,…,k } are non‐zero real numbers, is obtained. Furthermore, the behavior of solutions of the aforementioned system when p = 1 is examined. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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Anar T. Assanova Narkesh B. Iskakova Nurgul T. Orumbayeva 《Mathematical Methods in the Applied Sciences》2020,43(2):881-902
A periodic problem for the system of hyperbolic equations with finite time delay is investigated. The investigated problem is reduced to an equivalent problem, consisting the family of periodic problems for a system of ordinary differential equations with finite delay and integral equations using the method of a new functions introduction. Relationship of periodic problem for the system of hyperbolic equations with finite time delay and the family of periodic problems for the system of ordinary differential equations with finite delay is established. Algorithms for finding approximate solutions of the equivalent problem are constructed, and their convergence is proved. Criteria of well-posedness of periodic problem for the system of hyperbolic equations with finite time delay are obtained. 相似文献
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本文给出了常系数线性递推式（其中k是正整数,s=[（k＋1）／2]）以及交系数线性递推式的解的计算公式． 相似文献
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In this paper we are interested in a technique for solving some nonlinear rational systems of difference equations of third order, in three-dimensional case. Moreover, we study the periodicity of solutions for such systems. Finally, some numerical examples are presented. 相似文献
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This paper studies the nonautonomous nonlinear system of difference equations △x(n) = A(n)x(n) f(n, x(n)), n ∈ Z, (*)where x(n) ∈ RN,A(n) = (aij(n))N×N is an N × N matrix, with aij∈ C(R,R) for i,j =ω, z) = f(t, z) for any t ∈ R, (t, z) ∈ R × RN and ω is a positive integer. Sufficient conditions for the existence of ω-periodic solutions to equations (*) are obtained. 相似文献
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M. M. El‐Dessoky 《Mathematical Methods in the Applied Sciences》2015,38(15):3295-3307
This paper is devoted to study the periodic nature of the solution of the following max‐type difference equation: where the initial conditions x?2,x?1,x0 are arbitrary positive real numbers and is a periodic sequence of period two. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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Wei Gengping~ Shen Jianhua~ 《高校应用数学学报(英文版)》2006,21(3):320-326
This paper studies the nonautonomous nonlinear system of difference equationsΔx(n)=A(n)x(n)+f(n,x(n)),n∈Z,(*) where x(n)∈R~N,A(n)=(a_(ij)(n))N×N is an N×N matrix,with a-(ij)∈C(R,R) for i,j= 1,2,3,...,N,and f=(f_1,f_2,...,f_N)~T∈C(R×R~N,R~N),satisfying A(t+ω)=A(t),f(t+ω,z)=f(t,z) for any t∈R,(t,z)∈R×R~N andωis a positive integer.Sufficient conditions for the existence ofω-periodic solutions to equations (*) are obtained. 相似文献