Topological properties of the set of global solutions for a class of semilinear evolution equations in a Banach space. (English) Zbl 0627.47028
An abstract result about the topological properties of the set of fixed points of nonlinear operators on topological vector spaces is proved and is applied to the study of the Cauchy problem for various types of nonlinear differential equations in abstract spaces; e.g. in a Fréchet space under Carathéodory conditions and in a Banach space under Sobolev or Pazy’s assumptions.
Reviewer: G.Di Blasio
MSC:
47H10 | Fixed-point theorems |
47H20 | Semigroups of nonlinear operators |
34G20 | Nonlinear differential equations in abstract spaces |