Boundedness of solutions for sublinear reversible systems

Boundedness of Solutions for a Class of Sublinear Reversible Oscillators with Periodic Forcing

“…Furthermore, we also show that (8) has solutions of Mather type. The results obtained in [18][19][20] can be regarded as corollary of result of this paper. Remark 1.…”

“…Many fundamental results of the Hamiltonian systems possess reversible counterparts. On boundedness problem for sublinear reversible systems, the first results were obtained by Li [18], later, Yang [19], in the study of a sublinear reversible systems…”

Boundedness for sublinear reversible systems with a nonlinear damping and periodic forcing term

“…Theorem 1 in [29] can be regarded as a corollary of the boundedness result in the present paper when g( y) = y, τ = 3−α 1+α and j = 0. In fact, we denote β in [29] byβ, then β =β + 1 2 and α = p −1. The second inequality in (A2) is satisfied in this case, andβ = β − 1 2 > 1…”

“…Yang [29] also studied the boundedness of all solutions of (1.5). However, the results obtained in [14,29] have no information on unboundedness. In this paper, replacing the semilinear term ax + − bx − in (1.3) by a sublinear term γ |x| α−1 x, we are concerned with the boundedness and unboundedness of all solutions for sublinear second order differential equation with a nonlinear damping and periodic forcing term…”

“…5) In 2004, X.J. Yang [29] also studied the boundedness of all solutions of (1.5). However, the results obtained in [14,29] have no information on unboundedness.…”