算子方程组的正解及在半正微分边值系统的应用

POSITIVE SOLUTIONS FOR OPERATOR EQUATIONS SYSTEM AND APPLICATIONS TO SEMI-POSITONE DIFFERENTIAL SYSTEM

证明了半正算子方程组x=λK_1F_1(x,y),y=λK_2F_2(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,K_1,K_2:P→P为线性全连续算子,F_1,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.

In this paper, the existence of positive solutions for the operator equation system{x=λK1F1（x,y）y=λK2F2（x,y）is considered, where A 〉 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 λ〉 0 such that the operator equation system has at least one positive solution for 0 〈 λ 〈 λ. As an application, the existence of positive solutions of a semi-positone differential boundary value system is investigated.