2012
DOI: 10.1155/2012/508523
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Abstract: We show that the system of three difference equationsxn+1=an(1)xn-2/(bn(1)ynzn-1xn-2+cn(1)),yn+1=an(2)yn-2/(bn(2)znxn-1yn-2+cn(2)), andzn+1=an(3)zn-2/(bn(3)xnyn-1zn-2+cn(3)),n∈N0, where all elements of the sequencesan(i),bn(i),cn(i),n∈N0,i∈{1,2,3}, and initial valuesx-j,y-j,z-j,j∈{0,1,2}, are real numbers, can be solved. Explicit formulae for solutions of the system are derived, and some consequences on asymptotic behavior of solutions for the case when coefficients are periodic with period three are deduced.

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Cited by 54 publications
(73 citation statements)
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“…For some related cyclic systems of difference equations see [9,28,31] and [32], as well as some three-dimensional systems (see, e.g., [19,27,33]). Finally we note that, since difference equations have several applications in applied sciences, there exists a rich bibliography concerning theory and applications of difference equations (see ).…”
Section: Introductionmentioning
confidence: 99%
“…For some related cyclic systems of difference equations see [9,28,31] and [32], as well as some three-dimensional systems (see, e.g., [19,27,33]). Finally we note that, since difference equations have several applications in applied sciences, there exists a rich bibliography concerning theory and applications of difference equations (see ).…”
Section: Introductionmentioning
confidence: 99%
“…(for some extensions of the results, see [11,12], while the corresponding results for some related systems of difference equations can be found in [13]). Since that time, related transformations have been frequently used on difference equations ( [14][15][16]), as well as on close to symmetric systems (see [15,17,18] and numerous references therein), an area essentially initiated by Papaschinopoulos and Schinas (see [19][20][21][22][23][24][25]).…”
Section: Introductionmentioning
confidence: 99%
“…where coefficients (a n ) n∈N , (b n ) n∈N , and the initial value x 0 are real or complex (see [11][12][13][14][15]17,18,26,30]), which shows how useful the equation is (for how Equation (4) is solved, consult, for example, [3,8]; the book [3] has a nice explanation of three methods for solving it). Recently, we have studied several classes of product-type equations and systems (see [31][32][33][34] and the references therein), which cannot be directly solved by Equation (4), but behind their solvability is hidden the equation.…”
Section: Introductionmentioning
confidence: 99%
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“…Some generalizations of the equation, which are studied by developing the method, can be found in [8][9][10] (see also [11] where a slight extension of the equation was studied in another way). A related solvable system of difference equations was treated in [12]. Since that time various modifications of the method have been often used (see [13,14] and the references therein for some related difference equations, as well as [15][16][17] and the references therein for some related systems of difference equations).…”
Section: Introductionmentioning
confidence: 99%