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We study the following difference equation    x    n  +  1    =  (  p  +    x    n  -  1    )  /  (  q    x    n    +    x    n  -  1    )  ,  n  =  0,1  ,  …  ,  where  p  ,  q  ∈  (  0  ,  +  ∞  )  and the initial conditions    x    -  1    ,    x    0    ∈  (  0  ,  +  ∞  )  . We show that every positive solution of the above equation either converges to a finite limit or to a two cycle, which confirms that the Conjecture 6.10.4 proposed by Kulenović and Ladas (2002) is true.

abstract and applied analysis

Global Behavior of the Difference Equation<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:mi>p</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mo>(</mml:mo><mml…

Global Behavior of the Difference Equationxn+1=(p+xn-1)/(