On existence and uniqueness conditions for ordinary differential equations in Fréchet spaces. (English) Zbl 0880.34066

Herzog, G.

Stud. Sci. Math. Hung. 32, No. 3-4, 367-375 (1996).

Let \(F\) be a real or complex Fréchet space. Let \(\emptyset\neq D\subseteq F\) and let \(f:[0,T]\times D\to F\). Existence and uniqueness conditions are given for the solutions of the initial value problem \(u'(t)=f(t,u(t))\), \(u(0)=u_0\). The conditions are formulated as Lipschitz and one-sided Lipschitz conditions using a generalized distance and row-finite, monotone and quasimonotone matrices.

Reviewer: Tibor Krisztin (Szeged)

MSC:

34G20	Nonlinear differential equations in abstract spaces
47J25	Iterative procedures involving nonlinear operators

Keywords:

polynorm; row-finite matrix; quasimonotone; initial value problem