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Analytic solutions of a functional differential equation with a state derivative dependent delay. (English) Zbl 0959.34061

The authors consider analytic solutions to the state dependent functional-differential equation of the form \[ \alpha z+\beta x''(z)=x(az+bx''(z)), \] where \(\alpha\), \(\beta\), \(a\), \(b\) are complex numbers.
Existence theorems are established and the ways to deriving explicite solutions in different cases are shown.

MSC:

34K17 Transformation and reduction of functional-differential equations and systems, normal forms
34K23 Complex (chaotic) behavior of solutions to functional-differential equations
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