## Smooth solutions of a nonhomogeneous iterative functional differential equation with variable coefficients.(English)Zbl 0917.34055

The authors consider the nonhomogeneous iterative functional-differential equation with variable coefficients $x'(t)= \sum^m_{j=1} a_j(t) x^{[j]} (t)+F(t)$ with certain side conditions $$x^{(i)}(\tau)= \tau_i$$, $$i=0,1, \dots,m$$, and with $$a_j$$, $$F$$ given real functions. Here, $$x^{[0]}(t)=t$$, $$x^{[ 1]}= x(t)$$; $$x^{[k]}(t)= x(x^{[k-1]}(t))$$; $$k=2,3, \dots,m$$. Under assumptions, far too technical to be included here, and applying classical fixed point theorems, the authors obtain the existence of a solution.

### MSC:

 34K05 General theory of functional-differential equations 34K20 Stability theory of functional-differential equations
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### References:

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