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Stability in a nonlinear four-term recurrence equation. (English) Zbl 1068.39024
The authors consider the difference equation $x_{n+2} = f(x_{n+1}, x_n, x_{n-1}),\quad n = 0,1,\ldots,$ with initial conditions $$x_{-1}, x_0, x_{1} \geq 0$$ and $$x_{-1}^2 + x_0^2+ x_{1}^2 > 0.$$ Existence of unbounded solutions and the global attractivity of solutions are investigated.
MSC:
 39A11 Stability of difference equations (MSC2000) 39A12 Discrete version of topics in analysis 33C70 Other hypergeometric functions and integrals in several variables
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