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Qualitative behavior of difference equation of order two and positive nonoscillatory solutions
Khuong Vu Van
,
Thai Tran Hong
Abstract
In the paper we deal with the qualitative behavior of solutions of the following equation: $$x_{n+1}=ax_{n-1}-\dfrac{bx_n^2+cx_{n-1}^2}{1-dx_n+ex_{n-1}},\quad n=0,1,2,\dots$$ where the initial values $x_{−1},x 0$ are arbitrary positive numbers and $a,b,c,d,e$ are positive numbers. We also study the positive nonoscillatory solutions of the difference equation $$x_{n+1}=ax_{n-1}-\dfrac{bx_n^2+ax_{n-1}^2}{1-cx_n+x_{n-1}},\quad n=0,1,2,\dots.$$