A note on the solution of a class of two-point boundary value problems involving a mixed boundary condition (Q1206199)

In this short note the authors consider a class of two-point boundary value problems comprising nonlinear coupled differential equations involving \(m\) unknown functions defined over \((0,\infty)\) and linear boundary conditions. One of the boundary conditions depends linearly of a parameter \(k>0\). Assuming the given differential equation to be invariant under a certain transformation and assuming to have a solution corresponding to a particular value of the parameter the authors show that the solution for any other value of the parameter can be obtained by solving a polynomial equation. Some examples occuring in heat transfer problems are given.