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Addendum to periodic solutions of a third-order nonlinear differential equation. (English) Zbl 0777.34032

The author considers the nonlinear third order differential equation \[ x'''+ e(t,x,x',x'')a(t,x''')+ f(t,x,x',x'')b(t,x'')+ g(t,x,x',x'')c(t,x')+ h(t,x,x ',x'')=0,\tag{*} \] where \(e,f,g,h,a,b,c\) are continuous real functions of real variables and \(w\)-periodic with respect to \(t\). On these functions suitable assumptions are introduced and then some theorems on existence of a \(w\)-periodic solution \(x(t)\) to \((*)\) are proved. These theorems improve results by the same author [ibid. 97, 123-163, 165-195 (1990; Zbl 0754.34037; Zbl 0754.34038)].

MSC:

34C25 Periodic solutions to ordinary differential equations
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References:

[1] Vlček V.: Note on existence of periodic solution to the third-order nonlinear differential equation. Acta UPO, Fac.rer.nat. 97 (1990)) · Zbl 0754.34038
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