四阶差分方程在多点边值条件下解的存在性

Existence of Solutions for a Fourth Order Difference Equation with Multipoint Boundary Value Condition

运用Schauder不动点定理,考察了边值问题Δ4u(k-1)=g(k,u(k-1),u(k),u(k+1),u(k+2)),k∈Z(1,N)u(0)=A,u(N+1)=B,u(N+2)=C,u(N+3)=D解的存在性.

Schauder fixed--point theorem is applied to study the existence of solutions for the boundary value problem {△^4u（k-1）=g（k,u（k-1）,u（k）,u（k＋1）,u（k＋2））,k∈Z（1,N） u（0）=A,u（N＋1）=B,u（N＋2）=C,u（N＋3）=D