一种用于寻找二阶非瞬时脉冲抽象微分方程近似解的不动点方法
A fixed point approach for finding approximate solutions to second order non-instantaneous impulsive abstract differential equations
AI总结：
针对二阶非线性抽象微分方程的解逼近问题，采用投影算子构建有限维近似解，定义Faedo-Galerkin近似并结合余弦函数理论、Banach不动点定理等证明其存在性与收敛性，还给出了抽象公式示例。
摘要：
本文研究一类二阶非线性抽象微分方程的解的逼近问题。借助投影算子构建了给定系统的有限维近似解。我们探究了近似解与精确解之间的关联，以及收敛性问题。此外，我们定义了Faedo-Galerkin（F-G，法多-伽辽金）近似，并证明了其存在性与收敛性结果。这些结果是利用余弦函数理论、Banach不动点定理以及闭线性算子的分数幂得到的。最后，本文给出了一个抽象公式化的示例。
英文摘要：
This paper is concerned with the approximation of solutions to a class of second order non linear abstract differential equations. The finite-dimensional approximate solutions of the given system are built with the aid of the projection operator. We investigate the connection between the approximate solution and exact solution, and the question of convergence. Moreover, we define the Faedo-Galerkin(F-G) approximations and prove the existence and convergence results. The results are obtained by using the theory of cosine functions, Banach fixed point theorem and fractional power of closed linear operators. At last, an example of abstract formulation is provided.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
