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

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 \(W_2[0,\infty]\).

MSC:

34K05 General theory of functional-differential equations
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