Discussion on the analytic solutions of the second-order iterated differential equation. (English) Zbl 1131.34048

Liu, Hanze; Li, Wenrong

Bull. Korean Math. Soc. 43, No. 4, 791-804 (2006).

The paper deals with the second order differential equation with state-dependent argument \[ c_0 x''(z) + c_1 x'(z) + c_2 x(z) = x(az + bx(z)) + h(z), z \in \mathbb{C}, \eqno(1) \] where \(h\) is a given complex function, \(a,b\) and \(c_i, i=0,1,2,\) are complex numbers. Constructing analytic solutions for some auxiliary equation, the authors prove the existence of analytic solution for (1) in a neighborhood of the initial conditions \(x(0)=0, x'(0) = \alpha \neq 0.\)

Reviewer: Victor I. Tkachenko (Kyïv)

MSC:

34K05	General theory of functional-differential equations
34M05	Entire and meromorphic solutions to ordinary differential equations in the complex domain

Keywords:

differential equation with state-dependent argument; analytic solution