二阶差分系统正解的存在性

Existence of positive solutions for second-order difference system

依据Leray Schauder型非线性抉择对差分系统Δ2u1(k)+f1(k,u1(k),u2(k))=0 k∈[0,T]Δ2u2(k)+f2(k,u1(k),u2(k))=0 k∈[0,T]u1(0)=u1(T+2)=0=u2(0)=u2(T+2)给出了一个存在性定理.

By using a nonlinear alternative of LeraySchauder type, the existence of positive solutions to a secondorder difference system of boundaryvalue problems Δ2u1(k)+f1(k,u1(k),u2(k))=0k∈Δ2u2(k)+f2(k,u1(k),u2(k))=0k∈u1(0)=u1(T+2)=0=u2(0)=u2(T+2)is proved.