On ordinary differential equations in locally convex spaces. (English) Zbl 0612.34056

Lemmert, Roland

Nonlinear Anal., Theory Methods Appl. 10, 1385-1390 (1986).

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 \(E={\mathbb{R}}^ J\) (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:

34G10	Linear differential equations in abstract spaces
34C20	Transformation and reduction of ordinary differential equations and systems, normal forms
34G20	Nonlinear differential equations in abstract spaces
34A45	Theoretical approximation of solutions to ordinary differential equations
46A03	General theory of locally convex spaces

Keywords:

first order differential equations; comparison criteria; dissipativity condition; successive iterations

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