The positive solutions of abstract semilinear evolution equations and their applications. (Chinese. English summary) Zbl 0870.47040

Summary: The characteristics of positive operator semigroups in ordered Banach spaces are discussed. The supersolution and subsolution method for the study of ordinary differential equations and partial differential equations is applied to semilinear evolution equations in ordered Banach spaces. The results on the existence of the global solutions and positive solutions are obtained.


47H20 Semigroups of nonlinear operators
47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
47D06 One-parameter semigroups and linear evolution equations
47B65 Positive linear operators and order-bounded operators
46B40 Ordered normed spaces