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Zbl 0612.34056
Lemmert, Roland
On ordinary differential equations in locally convex spaces. (English)
[J] Nonlinear Anal., Theory Methods Appl. 10, 1385-1390 (1986). ISSN 0362-546X

The paper contains existence and uniqueness results for ordinary differential equations $u'(t)=f(t,u(t)),$ $u(0)=u\sb 0$ in locally convex Hausdorff spaces E. First, existence and comparison criteria are given for the linear autonomous case, if $E={\bbfR}\sp J$ (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.
[H.Engler]

MSC 2000:: *34G10 Linear ODE in abstract spaces
34C20 Transformation of ODE and systems
34G20 Nonlinear ODE in abstract spaces
34A45 Theoretical approximation of solutions of ODE
46A03 General theory of locally convex spaces

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

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