【摘要】 讨论了一类带有不确定自由项的非凸积分包含问题x(t)=λ(t,u)+∫t0f(t,s,u(s))ds,u(t)∈F(t,V(x)(t)))a.e.t∈[0,T],T>0解的存在性.利用集值映射的压缩原理和可测选择定理证明了在Lipschitz条件下上述积分包含问题的Filippov型存在定理,并且给出了逐点的Filippov型估计.对多值映射的选择空间赋予了一个较好的范数.将A.Cernea和Q.J.Zhu研究的关于积分包含结果从带有确定的自由项的情形推广到带有不确定自由项的情形.更多还原

【Abstract】 The existence of the solutions to a class of nonconvex integral inclusions with uncertain free term x（t）=λ（t,u）+∫ t₀f（t,s,u（s））ds,u（t）∈F（t,V（x）（t））) a.e. t ∈[0,T], T>0 is discussed. A Filippov type existence theorem of the integral inclusions with the Lipschitz conditions is verified using the contraction principle for set-valued maps and the measurable selection theorem. Furthermore a “pointwise” Filippov type estimate is given. An appropriate norm is also given to the selection space of the multifunction. This result mainly extends the conclusions of integral inclusions by A.Cernea and Q.J.Zhu from the case with certain free term to that with uncertain free term.更多还原