序Banach空间中一类算子方程的可解性

Solvability of a Class of Operator Equations in Ordered Banach Spaces

利用改进的Mnch紧性条件,研究了一类算子方程Lx=Nx的解的存在性．本文结果并没有要求算子L和N的连续性．作为应用,讨论了右端项不连续的隐式椭圆偏微分方程的边值问题的解的存在性．

In this paper, we investigate the existence of solutions for a class of operator equations Lx = Nx by using an improved weak compactness condition of MSnch. Here neither L nor N needs to be continuous. We also give some applications to boundary value problems of implicit elliptic differential equations with discontinuous right hand side.