Banach空间中非线性微分积分方程周期边值问题的一种拟上下解法

A Method of Quasi-Upper and Lower Solutions for Periodic Boundary Value Problems of Nonlinear Integro-differential Equations in Banach Spaces

利用L-拟上下解方法和混合单调迭代法,在适当的条件下,研究了Banach空间中一类非线性二阶微分积分方程周期边值问题解的存在性和惟一性,并给出了近似解的迭代序列和误差估计式.

By using the method of L-quasi-upper and lower solutions and the mixed monotone iterative technique, the problem of existence and uniqueness of solutions for periodic boundary value problems of a second order nonlinear integro-differential equations in Banach spaces is investigated, under appropriate conditions. Moreover, the iterative sequence and error estimate of approximation solutions are also given.