On a class of difference equations of monotone type. (Q1419753)

Let \(A\) be a maximal monotone multivalued operator acting in a Hilbert space, and \(c_i\), \(\theta_i\) positive constants. The author proves some existence and uniqueness theorems concerning the difference inclusion \(u_{i+1}-(1+\theta_i)u_i+ \theta_iu_{i-1}\in c_iAu_i+ f_i\) \((i\geq 1)\), \(u_0= a\), \(\sup_{i\geq 1}\| u_i\|< \infty\). Moreover, converging resp. periodic solutions are investigated, and an application to a partial difference equation is given.