Boundedness of semilinear Duffing equations with singularity

Abstract

We prove the boundedness of all solutions for the equation x″ + V′(x) = D_xG(x, t), where V(x) is of singular potential, i.e., lim_x→-1V(x) = +∞, and G(x, t) is bounded and periodic in t. We give sufficient conditions on V(x) and G(x, t) to ensure that all solutions are bounded.

Keywords

Hamiltonian system / repulsive singularity / boundedness of solutions / canonical transformation / Moser’s small twist theorem

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