半序空间中一类算子方程的可解性及应用

Solvability Theorems with Applications of an Operator Equation in Partial Order Space

本文在算子L和N都不必连续的情况下,利用锥理论和半序方法,在完备度量空间中和Banach空间中分别讨论了混合单调算子方程Lx=N(x,y)耦合拟解与解的存在性问题,构造出了新的非对称迭代序列研究了其逼近情况,得到了一些新的定理.最后,我们将所获得的结果应用于对Hammerstain非线性积分方程的解的存在性问题的研究.

In this paper,the theorem of cone and the techniques of partial order theory are used to discuss the existence of coupled quasi-solutions and solutions for a mixed monotone operator equation Lx=N（x,y） in complete metric space and Banach space,where neither L nor N need to be continuous.We also construct some new nonsymmetric iterative sequences and study their approximation,then we get some new theorems.Finally,we apply the new results presented in this paper to Hammerstain integral equations.