Why bvp4c always finds an eigenvalue (unknown parameter) equal to its initial guess?

Hello,

I have some experience with BVP solving with bvp4c, but this time I do not know what is going on.

I have a system of seven 1st-order ODE for y1(x) - y7(x). In each equation derivative of y(x) is equal to a linear combination of others y1(x) - y7(x), however with complicated x-dependent coefficients (mostly rational functions).

It is an eigenproblem with unknown parameter, 's' let's say. Almost all coefficients contain 's' in some powers, they are in fact rational functions of 's'. Thus the system is nonlinear in 's'.

Now my problem: bvp4c solves it, and solutions look reasonable I guess. However final eigenvalue is ALWAYS equal to the initial guess, or at least Matlab says so. Of course for different initial values of the eigenvalue there are different solutions of y(x). However it is hard to believe, that the spectrum of the eigenvalues is so dense :)

Does anyone have an idea where the problem might be? What does it mean in general, that final eigenvalue is always equal to its initial guess? Is it about the complicated dependence of the coefficients on the unknown parameter? Or is it something with boundary conditions, e.g. they are linearly dependent and the problem is underdetermined somehow?

I will be very grateful for any help or suggestions.

Best wishes,

Marek Gradzki