Lipschitz条件下脉冲微分方程的解

Solutions to Impulse Differential Equations under Lipschitz Conditions

研究Banach空间中非局部脉冲微分方程的解,在非局部项Lipschitz连续的条件下讨论微分方程适度解的存在性。主要利用Hausdorff非紧测度和不动点的方法,减弱这类问题的研究中对算子半群紧性的约束,在非紧半群条件下对脉冲函数紧性条件和Lipschitz条件做了统一处理,改进和推广了这一领域的相关结果。

This paper is concerned with the existence of nonlocal impulse differential equations under Lipschitz conditions in Banach spaces. By using the measure of non - compactness and fixed point theorem, the restric- tion on the compactness of operator semigroup is weakened. We deal with the cases of compactness and Lipschi- tz conditions for impulse functions in a unified way, which improves some related results in this area.