奇异二阶微分系统离散边值问题

Discrete Boundary Value Problems of Singular Second Order Differential Systems

利用锥不动点定理给出了奇异离散边值问题{Δ2x(i-1)+q1(i)f1(i,x(i),y(i))=0,i∈{1,2,…,T}Δ2y(i-1)+q2(i)f2(i,x(i),y(i))=0,x(0)=x(T+1)=y(0)=y(T+1)=0,的正解的存在性,其中非线性项fk(i,x,y)在(x,y)=(0,0)点奇异,k=1,2.

In this paper we investigates the existence of positive solutions to the singular discrete boundary value problem △^2x（i-1）＋q1（i）f1（i,x（i）,y（i））= 0,i∈{1,2 …,T},△^2y（i-1）＋q2（i）f2（i,x（i）,y（i））=0,x（0）=x（T＋1）=y（0）=y（T＋1）=0, by using cone fixed point theorem, where nonlinear term fk（i,x,y） is singular at （x,y） = （0,0）,k=1,2.