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Analytic solutions of a second-order functional differential equation with a state derivative dependent delay. (English) Zbl 0927.34077

This paper is concerned with a second-order functional-differential equation of the form \[ x''(z)=x(az+bx'(z)), \] where \(a\) and \(b\not = 0\) are complex numbers. A distinctive feature of this equation is that the argument of the unknown function depends on the state derivative. An existence theorem is established for analytic solutions and methods for deriving explicit solutions (in the form of power series) are given.
Reviewer: J.DiblĂ­k (Brno)

MSC:

34M05 Entire and meromorphic solutions to ordinary differential equations in the complex domain
34K23 Complex (chaotic) behavior of solutions to functional-differential equations
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