非混合单调二元算子方程(组)解的存在唯一性

Existence and Uniqueness of Solutions for(Systems of)Mixed Non-Monotone Binary Operator Equations

利用锥理论及Banach压缩映射原理,在不要求上、下解条件及算子紧性与连续性的条件下,建立了一类满足更一般序关系条件的非混合单调二元算子方程组(?)解的存在唯一性定理,以及非单调二元算子方程T(x,x)=x和非单调一元算子方程Lx=x解的存在唯一性定理,推广了最近相关文献的研究结果.

By using the cone theory and the Banach＇s contraction mapping principle, the existence and uniqueness theorems of solutions for a class of systems of mixed non-monotone binary operator equations as well as mixed non-monotone binary operator equations and unary operator equations in ordered Banach spaces under more general conditions with- out demanding the existence of upper and lower solutions and compactness and continuity conditions are established. The results in this paper generalize many known results.