I have a complex equation with multiple coefficients where some figures in the equation linearly and some not. By applying boundary conditions to the problem the determination of these coefficients become an eigenvalue problem that has infinitely many eigenvalues.

As far as I understand an approximation to the original equation is given by a series with eigenvalue_1, eigenvalue_2, ... inserted.

My question is where can I read more about this, what is the topic or the type of series that I might be thinking about and what is the form of such a series?

Please let me know if the information about the problem is insufficient.

Thanks in advance
regards Brian