Some new viability results for semilinear differential inclusions

摘要: Let X be a reflexive and separable Banach space, $ A : D(A) \subset \rightarrow $ the infinitesimal generator of C 0-semigroup S(t) X, t \geq 0 , D locally weakly closed subset in F 2^X nonempty, closed, convex bounded valued mapping which is weakly-weakly upper semi-continuous. The main result paper is:¶Theorem. Under general assumptions above necessary suffcient condition order that for each \xi \in there exists at least one mild solution u of¶¶ $ {du \over dt} (t) Au(t) + F(u(t)) ¶satisfying u(0) = so called "bounded w-tangency condition" below. (Bw {\cal TC}) . There function M} {\bf R}^*_+ enjoying property exists y F(\xi) such \delta \gt each weak neighborhood V exist ({\rm 0},\delta ] and p with \parallel \leq M}(\xi) satisfying¶¶ S(t)\xi t(y p) D.