On some nonlocal evolution equations in Banach spaces

This note is concerned with the initial value problem for the abstract nonlocal equation (Au)' + (Bu) There Exists f where A is a maximal monotone operator from a reflexive Banach space E to its dual E*, while B is a nonlocal maximal monotone operator from L-p (0, T; E) to L-q (0, T; E*) with p(-1) + q(-1) = 1, p is an element of (1, infinity). Under proper boundedness and coercivity assumptions on the operators, a solution is achieved by means of a discretization argument. Uniqueness and continuous dependence are also discussed and we prove some estimates for the discretization error. Finally, we deal with the approximation of linear Volterra integrodifferential operators.