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Abstract
Evolution equations of the type: (UNFORMATTED TABLE FOLLOWS)
(E) x' + A(t)x (CONT) f(t), t (ELEM) 0,T ,
x(0) = x(,o)
(TABLE ENDS)
are studied.
The underlying space is a general Banach lattice. The operators A(t)u are maximal lattice accretive (mL-accretive) in u and satisfy a weak smoothness condition in t. The function f(t) is an L('1)-function.
Recent results of Evans concerning general Banach spaces are extended to the present case. Namely, an evolution operator is generated for the problem (E) via a difference scheme. Functionals involving the Gateaux derivative of the norm play an important role in the development of theory.
Some applications are given in the theory of non-linear partial differential equations.
