Banach空间中二阶非线性脉冲微分方程初值问题解的存在性

利用Monch不动点定理和分段估计方法,结合Gronwall不等式,研究了Banach空间中一类二阶非线性脉冲微分方程初值问题解的存在性。将该问题转化为等价的一阶非线性脉冲积分方程,在较弱的非紧性条件和先验估计条件下,获得了其解的存在性充分条件,改进和推广了相关文献的结果。

Existence of Solutions for a Class Initial Value Problems of Second-Order Nonlinear Impulsive Differential Equations in Banach Spaces

By using the Monch fixed theorem and a piece wise estimation method, and combining with a Gronwall inequality, a class initial value problems of second-order nonlinear impulsive differential equations in Banach Spaces is investigated, which can be reduced to the equivalent first-order nonlinear impulsive integral equation. Under weaker noncompactness and priori esti-mate conditions, some sufficient results on the existence of solution for the initial value problem are established. Some known re-sults are extended and improved.