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- W2912142456 abstract "Abstract In this paper, we determine the forbidden sets, introduce an explicit formula for the solutions and discuss the global behaviors of solutions of the difference equations <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mtable> <m:mtr> <m:mtd> <m:mstyle> <m:msub> <m:mi>x</m:mi> <m:mrow> <m:mi>n</m:mi> <m:mo>+</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>=</m:mo> <m:mfrac> <m:mrow> <m:mi>a</m:mi> <m:msub> <m:mi>x</m:mi> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msub> <m:msub> <m:mi>x</m:mi> <m:mrow> <m:mi>n</m:mi> <m:mo>−</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> </m:mrow> <m:mrow> <m:mi>b</m:mi> <m:msub> <m:mi>x</m:mi> <m:mrow> <m:mi>n</m:mi> <m:mo>−</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>+</m:mo> <m:mi>c</m:mi> <m:msub> <m:mi>x</m:mi> <m:mrow> <m:mi>n</m:mi> <m:mo>−</m:mo> <m:mn>2</m:mn> </m:mrow> </m:msub> </m:mrow> </m:mfrac> <m:mo>,</m:mo> <m:mspace /> <m:mi>n</m:mi> <m:mo>=</m:mo> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:mn>1</m:mn> <m:mo>,</m:mo> <m:mo>…</m:mo> </m:mstyle> </m:mtd> </m:mtr> </m:mtable> </m:math> $$begin{array}{} displaystyle x_{n+1}=frac{ax_{n}x_{n-1}}{bx_{n-1}+ cx_{n-2}},quad n=0,1,ldots end{array} $$ where a , b , c are positive real numbers and the initial conditions x −2 , x −1 , x 0 are real numbers." @default.
- W2912142456 created "2019-02-21" @default.
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- W2912142456 date "2019-01-22" @default.
- W2912142456 modified "2023-09-25" @default.
- W2912142456 title "Global behavior of two third order rational difference equations with quadratic terms" @default.
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- W2912142456 doi "https://doi.org/10.1515/ms-2017-0210" @default.
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