Upper and lower solutions method for existence of periodic solutions of Duffing equation (Q2721847)

Consider the Duffing-type equation (*) \(x''+kx' +g(t,x)=s\), where \(g\) is a Carathéodory function, \(k\neq 0\) and \(s\) are real parameters. Using the method of upper and lower solutions and the Leray-Schauder continuation theorem, the author derives conditions guaranteeing the existence of at least one periodic solution for some \(s\)-interval. The author extends results due to \textit{C. Fabry}, \textit{J. Mawhin} and \textit{M. N. Nkashama} [Bull. Lond. Math. Soc. 18, 173-180 (1986; Zbl 0586.34038)] and \textit{I. Rachunková} [Nonlinear Anal. Theory Methods Appl. 18, No. 5, 497-505 (1992; Zbl 0756.34026)].