本文利用上下解方法与正算子半群理论，讨论了Banach空间中具有混合单调（混拟单调）性质的非线性发展方程耦合周期解的存在性及周期解的存在唯一性，所得结果概括并推广了有关常微分方程和偏微分方程的若干结论．

In this paper, the supsolution and subsolution method and the positive op erators semigroups theory are applied to periodic solution problems for semilinear evo lution equations with mixed monotone or mixed quasimonotone nonlinear terms in Ba nach spaces. The results on the minimal and maximal coupled periodic (qusi)solution are obtained. These results generalize and extend the relevant results in ordinary differential equations and partial differential equations.