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We study global behavior of the following max-type difference equation xn+1=max⁡{1/xn,An/xn−1}, n=0,1,…, where {An}n=0∞ is a sequence of positive real numbers with 0≤inf⁡An≤sup⁡An<1. The special case when {An}n=0∞ is a periodic sequence with period k and An∈(0,1) for every n≥0 has been completely investigated by Y. Chen. Here we extend his results to the general case

abstract and applied analysis

Global Behavior of the Max-Type Difference Equation<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>x</mml:mi><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:mi>max</mml:mi><mml:mo>⁡</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>A</…

Global Behavior of the Max-Type Difference Equationxn+1=max⁡{1/xn,A