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Solution with periodic second derivative of a certain third order differential equation. (English) Zbl 0629.34048
Sufficient conditions for the existence of periodic solutions of the third kind, i.e. those with the second periodic derivative, to the equation \(x\prime''+ax''+g(t,x')+cx=p(t)\), where a, c are constants, \(g(t,y+w)\equiv g(t+T,y)\equiv g(t,y)\in {\mathfrak C}^ 1(R^ 2)\) and p(t)\(\in {\mathfrak C}^ 1({\mathbb{R}}^ 1)\) is of the special (necessary) form, are given using a topological degree argument. This problem is solvable for \(0\neq | c| <| T|^{-3}\).

MSC:
34C25 Periodic solutions to ordinary differential equations
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References:
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