## Asymptotic solutions for second order delay differential equations.(English)Zbl 0871.34045

We study asymptotic formulae for the solutions of the second order delay-differential equations $u''(t)+ b(t)u(t- r(t))=0$ and $(a(t)u'(t))'+ b(t)u(t-r(t))=0.$ More generally, consider the second order functional differential equation $(a(t)u'(t))'+ b(t)f(t,u(t-r(t)))=0,$ where the functions $$a,b: [0,\infty)\to (0,\infty)$$, $$f:[0,\infty)\times \mathbb{R}\to \mathbb{R}$$ and $$r:[0,\infty)\to [0,r_0]$$ (for some $$r_0$$) are continuous.

### MSC:

 34K25 Asymptotic theory of functional-differential equations 34B27 Green’s functions for ordinary differential equations
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### References:

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