向量半线性二阶脉冲泛函微分包含的C^1-可解性

C^1-Solvability Criteria for Vector Semilinear Second-Order Impulsive Functional Differential Inclusions

本文在可分Banarch空间上研究了一类具局部条件与多值脉冲特征的二阶半线性中立型泛函微分包含,利用算子分裂方法、算子的余弦族理论及关于多值映射的Dhage不动点定理,分别给出当微分包含的多值非线性项是全连续映射与Lipschitz连续映射时C1-解的两个存在性定理,去掉了以往相关结果中关于余弦族的多余的紧性限制·

A semilinear second-order neutral functional differential inclusion with nontocal conditions and multivalued impulse characteristics in a separable Banach space is considered. Two existence theorems for Cl-solutions are given, when the multivalued nonlinearity of the inclusion is a Lipschitz continuous map and a completely continuous map, respectively. The results are obtained by using operator splitting method, the theory of continuous cosine families of bounded linear operators and the fixed point theorem for multivalued maps due to Dhage. The crucial compactness restriction on the cosine family is removed from previous results.