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Oscillation of forced nonlinear second order self-adjoint difference equations. (English) Zbl 1044.39010
Oscillatory behavior and disconjugacy of solutions are studied for the following second order linear homogeneous difference equations: $\Delta(p(n-1)\Delta y(n-1)) + q(n)y(n) = 0$ $c(n)y(n+1) - b(n)y(n) + c(n-1)y(n-1) = 0$ $y(n+1) + \alpha(n)y(n) + \beta(n)y(n-1) = 0$ The first two ones are in self adjoint form and the third one may be given in this form for $$\beta(n)>0$$. The results concerning the second equation involve conditions in terms of the coefficients and can be easily translated in conditions on the third equation provided $$\beta(n)>0$$. The author considers the case $$\beta(n)<0$$ when the third equation cannot be given in the self-adjoint form.
The migration of the results from the second to the third equation is not straightforward.

##### MSC:
 39A11 Stability of difference equations (MSC2000)