Oscillation of forced nonlinear second order self-adjoint difference equations (Q1425602)

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.