Existence and stability for a nonlinear model describing arctic gyres (Q6593185)

The flow of the Arctic gyres can be described as second-order ordinary differential equations with some related conditions. In this paper, the author investigated a more general second-order ordinary differential equation with the asymptotic conditions and the boundary condition which arise from the study of Arctic gyres. By using Banach's contraction principle, they established an existence and uniqueness of the bounded solution to the equation when the nonlinearity \(f\) is Lipschitz-like continuous. Moreover, they provided a stability for the bounded solution. And they also obtained an existence result for the continuous nonlinear vorticity term by Schauder's fixed point theorem.