抽象半线性发展方程初值问题的整体解

The Global Solutions of Initial Value Problem for Abstract Semilinear Evolution Equations

在抽象空间框架下，研究了具有广泛物理背景的一类半线性发展方程初值问题整体解的存在性．利用正算子半群特征与凸锥理论，把上下解方法引入该问题，给出了整体解存在及唯一的若干充分条件．所得的结果概括、统一及推广了常微分方程、偏微分方程及Ｂａｎａｃｈ空间常微分方程中的有关结论．

spaces. Some existence and uniquence theorems of global solutions are shown by using the characteristics of positive operators semigroups and convexcone theory. The present results generalize, unify and extend the relevant conclusions in ordinary differential equations, partial differential equations and abstract ordinary differential equations.