## On the existence of solutions of some second order nonlinear difference equations.(English)Zbl 1122.39001

The authors study the second order difference equation $\Delta ^2 y_n = a_n y_{n+1} + f(n,y_n,y_{n+1}),\quad n\in N. \tag{E}$ They give two theorems ensuring the existence of a solution $$y$$ of equation (E) such that $$y_{n+1} = \alpha _{n}u_n + \beta _{n}v_n,$$ where $$\lim \alpha _n=\alpha$$, $$\lim \beta _n=\beta$$, $$\alpha , \beta \in \mathbb R$$ and $$u$$, $$v$$ are solutions of the equation $$\Delta ^2 z_n = a_{n+1} z_{n+1}.$$

### Keywords:

nonoscillatory solution
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