Well posedness for evolution inclusions

[摘要] We prove the existence of a continuous selection of the multivalued mapφ→Φ(φ)which is the set of all mild solutions of the evolution inclusionx(t)∈Ax(t)+F(t,x(t))+∫0th(t−s)g(x(s))dsx(0)=φ.HereFis a multivalued map, Lipschitzian with respect tox, andAis the infinitesimal generator of aC0-semigroup.

[学科分类] 应用数学