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Periodicity and stability of solutions of higher order rational difference equation. (English) Zbl 1169.39001

This paper is concerned with the recurrence relation

x n+1 =a+dx n-l x n-k b-cx n-s ,n=0,1,2,,(1)

where a,b,c,d are positive constants, together with given positive initial values x -r ,x -r+1 ,,x 0 , all different from b/c (where l,k,s are nonnegative integers and r=max{l,k,s}).

Existence criteria for positive prime period two solutions is given. Sufficient conditions for the existence of equilibrium points and their asymptotic stability are also given. Two explicit solutions for special cases of (1) are also derived.


MSC:
39A11Stability of difference equations (MSC2000)
39A20Generalized difference equations