Analytic solutions to a class of nonlinear infinite-delay-differential equations. (English) Zbl 1160.34059

Lü, Xueqin; Cui, Minggen

J. Math. Anal. Appl. 343, No. 2, 724-732 (2008).

The analytic solutions of the infinite delay differential equation with proportional delay \[ u'(x)=g(x,u(x),u(px)),\quad u(0)=\eta,\quad (p\in (0,\,1)) \] are studied, based on the characteristics of the reproducing kernel space \(W_2[0,\infty]\).

Reviewer: Ivan Ginchev (Varese)

MSC:

34K05

General theory of functional-differential equations

Keywords:

infinite-delay-differential equations; exact solutions; reproducing kernel space

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