×

Periodic solutions of second order neutral equations. (Chinese. English summary) Zbl 0792.34070

After expanding a \(2 \pi\)-periodic function \(f \in C^ 1(R,R)\) into a Fourier series the author makes an assumption that the equation \(x''(t)+\sum^ 2_{i=1} a_ ix^{(2-i)} (t)+\sum^ 2_{i=0} c_ ix^{(2-i)} (t-h)=f(t)\) has a solution in the form \(x(t)=b_ 0+\sum^ \infty_{n=1} (b_ n \cos nt+l_ n \sin nt)\) and then deduces a necessary and sufficient condition for the existence of such a solution.

MSC:

34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34K40 Neutral functional-differential equations
34C25 Periodic solutions to ordinary differential equations
PDFBibTeX XMLCite