算子方程组的正解及在半正微分边值系统的应用

证明了半正算子方程组{x=λK1F1(x,y),y=λk2f2(x,y)正解的存在性结果,其中λ>0为参数,P为实Banach空间E中一个完全锥,K1,K2:P→P为线性全连续算子,F1,F2:P→E为连续有界算子.作为应用,给出了一类半正微分边值系统正解存在性的结果.

Positive Solutions for Operator Equations System and Applications toSemi-Positone Differential System

In this paper, the existence of positive solutions for the operator equation system $$ \left\{ \begin{array}{l}x=\lambda K_1 F_1(x, y), y=\lambda K_2 F_2(x, y), \end{array} \right. $$is considered, where $\lambda>0$ is a parameter, $P$ is a total cone of the real Banach space $E$. Under some superlinear conditions it is shown that there exists $\lambda^*>0$ such that the operator equation system has at least one positive solution for $0<\lambda\leq \lambda^*$. As an application, the existence of positive solutions of a semi-positone differential boundary value system is investigated.