Boundedness of solutions of a quasi-periodic sublinear Duffing equation
In this paper, the authors study the Lagrangian stability for the sublinear Duffing equations \(x''+e(t)|x|^{\alpha-1}x=p(t)\) with \(0<\alpha<1\), where \(e\) and \(p\) are real analytic quasi-periodic functions with frequency \(\omega\). By using the invariant curve theorem for quasi-periodic mappings established by \textit{P. Huang} et al. [Nonlinearity 29, No. 10, 3006--3030 (2016; Zbl 1378.37078)], they prove that every solution of the equation is bounded provided that the mean value of \(e\) is positive and the frequency \(\omega\) satisfies a Diophantine condition.
scientific article; zbMATH DE number 7344775
scientific article