Lee, John W.; O’Regan, Donal Existence results for differential delay equations. I. (English) Zbl 0782.34070 J. Differ. Equations 102, No. 2, 342-359 (1993). 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. Reviewer: T.Dłotko (Katowice) Cited in 1 ReviewCited in 27 Documents MSC: 34K05 General theory of functional-differential equations Keywords:Carathéodory solutions of delay differential equations; Leray-Schauder method; existence theorems; nonlinear alternative; initial value problems Citations:Zbl 0782.34069 PDFBibTeX XMLCite \textit{J. W. Lee} and \textit{D. O'Regan}, J. Differ. Equations 102, No. 2, 342--359 (1993; Zbl 0782.34070) Full Text: DOI