Explain the determine green and the information ti here The objective of this article is to investigate somequalitative behavior of the solutions of the nonlineardifference equationbxn– kX+1 = Axn+ Bxp–k+CXp-1+Dxp-o+[dxn-k– ex-1(1)n= 0, 1,2, .....where the coefficients A, B, C, D, b, d, e e (0,00), whilek, 1 and o are positive integers. The initial conditionsX-g,..., X_1,..., X_ k, ..., X_1, Xo are arbitrary positive realnumbers such that k < 1 < 0. Note that the special casesof Eq. (1) have been studied in [1] when B= C= D= 0,and k = 0,1= 1, b is replaced byB=C= D=0, and k= 0, b is replaced by – b and in[33] when B = C = D = 0, 1= 0 and in [32] whenA= C= D=0, 1=0, b is replaced by – b.••..- b and in [27] when6. Theorem 10. If 1 is even and k, o are odd positive integers,then Eq. (1) has prime period two solution if the condition(А+ C) (Зе— d) < (е+ d) (1-(В+ D),(29)isvalid,(B+ D)andprovidedd (1 — (В+ D) — е (А+С)>0.< 1Proof.If 1 is even and k,are odd positive integers, thenXn = Xp–1 and xn+1 = Xn-k = Xn-o. It follows from Eq.(1)thatbPР- (А+C)Q+ (B+D) P —(30)(e Q– dP)'andbQQ= (A+C) P+(B+D) Q –(31)(e P- dQ)'Consequently, we getbP+Q=(32)[d (1 — (В+ D)) — е (А+С)]"where d (1– (B+D)) – e (A+C) > 0,e b² (A+C)PQ=(e+d) [K2+(A+ C)][d K2 – e (A+C)]²"(33)-where K2(1– (B+D)), provided (B+ D) < 1.Substituting (32) and (33) into (28), we get the condition(29). Thus, the proof is now completed.O

Name: Explain the determine green and the information ti here The objective
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Description: Explain the determine green and the information ti here The objective of this article is to investigate somequalitative behavior of the solutions of the nonlineardifference equationbxn– kX+1 = Axn+ Bxp–k+CXp-1+Dxp-o+[dxn-k– ex-1(1)n= 0, 1,2, .....whe