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Abstract. In this paper we study the behavior of the difference equation $$ x_{n+1}=ax_{n}+{bx_{n}x_{n-2}\over cx_{n-1}+dx_{n-2}}, n=0,1,\ldots, $$ where the initial values $x_{-2}$, $x_{-1}$, $x_{0}$ are arbitrary positive real numbers and $a$, $b$, $c$, $d$ are positive constants. Also, we give the solution of some special cases of this equation.
AMS Subject Classification
(1991): 39A10
Keyword(s):
stability,
boundedness,
solution of difference equations
Received December 19, 2007, and in final form June 6, 2008. (Registered under 6064/2009.)
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