On the existence theorem of an eigenvalue problem arising from hydrodynamics

An investigation concerning the relations between the solutions of the full Navier-Stokes equations and the boundary layer equations conducted by Guderley and Wen (1973) is considered, taking into account a set of simple model equations for a two-dimensional incompressible viscous flow in a channel. The equations represent an eigenvalue problem which is not of the classical Sturm-Liouville type. An existence theorem for the eigenvalue problem is discussed. It is shown that a denumerable set of eigenvalues and eigenfunctions exists for the above problem.