Some new results for a second-order differential equation arising from a mathematical model related to the Antarctic Circumpolar Current

In this paper, we study the existence and uniqueness of solutions of a second-order differential equation arising from the Antarctic Circumpolar Current (ACC) and the Ulam–Hyers stability under different ocean vorticity cases. Firstly, we present the expression of general solution for constant vorticity. Secondly, by constructing a new Green’s function corresponding to a second-order ordinary differential equation, which is related to the boundary conditions. Finally, we demonstrate the existence and uniqueness of solution in cases of linear vorticity and nonlinear vorticity.