GEOMETRIC ANALYSIS OF A NONLINEAR BOUNDARY-VALUE PROBLEM FROM PHYSICAL OCEANOGRAPHY

A third-order nonlinear differential equation with two sets of boundary conditions is considered. These boundary value problems arise as boundary layer problems from a model of large scale ocean circulation. Using geometrical techniques from qualitative differential equations, such as Wazewski's theorem, invariant manifolds, and Lyapunov functions, the existence of solutions for each boundary value problem is given in a uniform way for all positive values of a parameter of the differential equation.