## Existence of regularly varying solutions with nonzero indices of half-linear differential equations with retarded arguments.(English)Zbl 1189.34121

Summary: Sharp conditions are established for the existence of a pair of regularly varying solutions with nonzero indices of half-linear functional differential equations of the type $(|x'(t)|^{\alpha}\text{sgn }x'(t))'=q(t)|x(g(t))|^{\alpha}\text{sgn }x(g(t)),~\alpha>0,~g(t)>0,~g(t)<t.$

### MSC:

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

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