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Existence results for differential delay equations. I. (English) Zbl 0782.34070

The equation \[ y^{(k)}(t)= F(t,y(s_{11}(t)),\ldots,y(s_{1m_ 1}(t)),\ldots,y^{(k-1)}(s_{k1}(t)),\ldots,y^{(k-1) }(s_{km_ k}(t))),\;t\in [0,T], \] with \(F\) continuous or a Carathéodory function is considered. Both cases are treated together. By transversality theorem or Schauder-Leray principle existence theorems (in form of the nonlinear alternative) of initial value problems are demonstrated. Examples connected with generalization of Riccati equation are discussed.

MSC:

34K05 General theory of functional-differential equations

Citations:

Zbl 0782.34069
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