反向上下解条件下的非线性算子的不动点定理

Fixed Point Theorems of Nonlinear Operators with Counter Upper-down Solution Condition

利用锥定义空间中的半序,通过引进完全相对σ-完备集这一概念得到满足反向上下解条件(Au0≤u0 <v0≤Av0)增算子A的多个不动点存在性定理以及满足反向上下解条件(A(u0,v0)≤u0<v0≤A(v0,u0))混合单调算子A的耦合不动点定理。

The multiple fixed point theorem of increasing operator and coupled quasi-fixed point theorem of mixed monotone operator which satisfy the counter upper-down solution condition are studied by using the complete relative siva-complete set. The partial ordering is defined by a cone of the real Banach space.