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

Li, Yongxiang

Acta Math. Sin. 39, No. 5, 666-672 (1996).

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.

MSC:

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

Keywords:

positive operator semigroups; ordered Banach spaces; supersolution; subsolution; ordinary differential equations; partial differential equations; semilinear evolution equations