## Periodic solutions of differential-delay equations with more than one delay.(English)Zbl 0644.34064

This paper deals with the existence of nontrivial periodic solutions of differential-delay equations of the form $$x'(t)=-\alpha \sum^{N}_{i=0}\lambda_ if(x(t-p_ i)).$$ The method of proof involves techniques which have been used to study differential-delay equations with a single delay and to show how these techniques can be generalized. These results also imply a nonuniqueness result for so- called “slowly oscillating” periodic solutions of the equation $$x'(t)=- \alpha \sum^{N}_{i=1}f(x(t-i))$$ studied by other authors.
Reviewer: R.S.Dahiya

### MSC:

 34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument) 34C25 Periodic solutions to ordinary differential equations
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