Boundedness of solutions for a class of sublinear reversible oscillators with periodic forcing
Summary: We study the boundedness of all solutions for the differential equation \[ x''+f(x)x'+(B+\varepsilon e(t))|x|^{\alpha -1}x=p(t), \] where \(f(x)\), \(p(t)\) are odd functions, \(e(t)\) is an even function, \(e(t)\), \(p(t)\) are smooth 1-periodic functions, \(B\) is a nonzero constant, and \(\varepsilon\) is a small parameter. A sufficient and necessary condition for the boundedness of all solutions of the above equation is established. Moreover, the existence of Aubry-Mather sets is obtained as well.
scientific article; zbMATH DE number 6306558