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Global behavior of a higher order difference equation. (English) Zbl 1186.39024

Summary: We study the asymptotic stability of the nonnegative equilibrium points of the difference equation

x n+1 =Ax n-1 /(B+C i= k x n-2i ),n=0,1,

where A,B,C are nonnegative real numbers and ,k are nonnegative integers, k. We discuss the conditions under which there exist prime period two solutions and semicycles. Finally we investigate the oscillation and the existence of unbounded solutions.

39A30Stability theory (difference equations)
39A20Generalized difference equations
39A21Oscillation theory (difference equations)
39A22Growth, boundedness, comparison of solutions (difference equations)
39A23Periodic solutions (difference equations)