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

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