FUNCTIONAL EVOLUTION EQUATIONS INVOLVING T-ACCRETIVE AND T-LIPSCHITZ OPERATORS IN BANACH LATTICES

Evolution equations of the type: (E) x' + A(t)x = G(t,x(,t)), t (ELEM) {0,T}, x(t) = (phi)(t), t (ELEM) {-r,0} are investigated.

The underlying space X is a Banach Lattice with a uniformly convex dual space X*. The operator A(t) is the sum of a demicontinuous generalized T-accretive operator and an MT-accretive operator for every t (ELEM) {0,T}. For each u (ELEM) D(A(t)) (TBOND) D, A(t)u satisfies a smoothness condition with respect to t. The function G(t,(psi)) is a global Lipschitzian.

Recent results of Calvert concerning the autonomous unperturbed case are extended.

Two of the main results of the thesis are new even in the accretive case and extend recent associated results of the Kartsatos and Parrott.

Applications are given at the end of the theses.