非连续增算子的不动点定理及其应用

Fixed Point Theorems for Discontinuous Increasing Operators and Applications

给出了Banach空间的一个增算子不动点定理,将这一定理应用到Banach空间含间断项的二阶非线性脉冲积-微分方程,给出了一类方程的最大解和最小解的存在性定理.应用以上2个定理并通过建立比较定理,讨论了Banach空间含间断项的二阶非线性脉冲积-微分方程的初值问题的最大解、最小解的存在性,并且在应用定理时仅用锥正规,减弱了刘笑颖等提出的锥正则条件.

in this paper, a new fixed point theorem for discontinuous increasing operator in Banach Spaces is derived. The theorem is applied to the second order discontinuous nonlinear impulsive integro-differential equations in Banach spaces, and the result about the existence of its maximal and minimal solutions is obtained. The initial value problems for second order discontinuous nonlinear impulsive integro-differential equations in Banach spaces are investigated. By establishing comparison theorems and using a fixed point theorem, the existence of maximal and minimal solutions is proved. The findings in this paper generalize and improve the relevant results presented in some well-known prestigious literatures.