Bounded solutions of a nonlinear second order differential equation with asymptotic conditions modeling ocean flows

We investigate the existence and uniqueness of bounded solutions to a nonlinear second order differential equation with asymptotic conditions. Such asymptotic conditions arise in the study of the ocean flow in arctic gyres. We derive an equivalent formulation of the problem in the form of an integral equation on a semi-infinite interval, and then use fixed point techniques. In the case of Lipschitz continuous nonlinearities, we also obtain a stability result.