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Periodic solutions for a third order differential equation under conditions on the potential. (English) Zbl 0923.34045

The existence of (harmonic) periodic solutions is proved for the equation \[ x'''+ ax''+ g(x')+ cx= p(t), \] where \(g\) is continuous, \(p\) is periodic and Lebesgue integrable over the period, \(a\) is a constant and \(c\neq 0\). Sufficient conditions are obtained by means of the standard Leray-Schauder degree technique. They are mainly related to the asymptotic behaviour of the primitive of \(g\). The result generalizes some of its analogies of other authors quoted among the references.
Reviewer: J.Andres (Olomouc)

MSC:

34C25 Periodic solutions to ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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