A survey of local existence theories for abstract nonlinear initial value problems
作者： Eric Schechter
DOI: 10.1007/BFB0086759
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摘要: This paper surveys the abstract theories concerning local-in-time existence of solutions to differential inclusions, u′(t)∈F(t,u(t)), in a Banach space. Three main approaches assume generalized compactness, isotonicity an ordered space, or dissipativeness. We consider different notions “solution,” and also importance assuming not that F(t, x) is continuous x. Other topics include Caratheodory conditions, uniqueness, semigroups, semicontinuity, subtangential limit solutions, dependence u on F, bijections between F.
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