在L,N都不必连续的情况下,利用半序方法,研究了算子方程Lx=Nx的可解性,得到了该方程在完备度量空间与Banach空间中解的存在性与多解性结果,并将所获结果应用于一个微分-积分方程的周期边值问题.

In this paper, the techniques of partial order theory are used to study the solvability of a class of operator equations Lx = NX, where neither L nor N need to be continuous. Existence and multiplicity results are obtained in complete metric space and Banach space respectively, and then applied to a periodical boundary value problem of an intergro-differential equation.