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On ordinary differential equations in locally convex spaces. (English) Zbl 0612.34056
The paper contains existence and uniqueness results for ordinary differential equations u ' (t)=f(t,u(t)), u(0)=u 0 in locally convex Hausdorff spaces E. First, existence and comparison criteria are given for the linear autonomous case, if E= J (J a general index set) with the product topology. In the general case, a dissipativity condition for f in terms of the system of seminorms that generate the topology of E is assumed, implying that successive iterations converge by the results for the linear case.
Reviewer: H.Engler
MSC:
34G10Linear ODE in abstract spaces
34C20Transformation and reduction of ODE and systems, normal forms
34G20Nonlinear ODE in abstract spaces
34A45Theoretical approximation of solutions of ODE
46A03General theory of locally convex spaces