Linearization of coupled second-order nonlinear ordinary differential equations (SNODEs) is one of the open and challenging problems in the theory of differential equations. In this paper, we describe ...

We investigate the asymptotic properties as t → ∞ of the following differential equation in the Hilbert space H: $\ddot x(t) + a(t)\dot x(t) + \nabla G(x(t)) = 0,t \ge 0,$ where the map \[\mathbb{R}_ ...