无穷区间上一类不连续非线性积分方程的唯一解

The Unique Solution for Discontinuous Nonlinear Integral Equations on Infinite Interval

在一般Banach空间中研究了一类无穷区间上不连续非线性积分方程的唯一解.在非常弱的条件下证明了非线性积分方程的唯一解可以由迭代序列的一致极限得到,并给出了逼近解的迭代序列的误差估计式,然后应用到无穷区间一阶微分方程的终值问题,本质改进(将紧型条件删去)并推广了一些结果.

The unique solution of the discontinuous nonlinear integral equations in Banach spaces are investigated. In very weakly condition, the unique solution of nonlinear integral equations can be obtained by the uniformly limit of the iterative sequences is proved. The error estimate of the iterative sequences of approximation solutions is given. And then apply this result to the terminal value problems of first order differential equations. The results obtained here improve and extend some corresponding results.