Boundedness for sublinear Duffing equations with time-dependent potentials
The author considers the sublinear second order differential equation with time-dependent potential: \[ \ddot {x} + e(t|x|^{\alpha-1}x= p(t), \tag{1} \] where \(0<\alpha<1\), \(p(t)\) and \(e(t)\) are smooth 1-periodic functions. A necessary and sufficient condition has been proved for the boundedness of all solutions of (1).
scientific article; zbMATH DE number 5563785