We consider a general class of eigenvalue problems with two-point boundary
conditions on a finite interval generated by a differential equation with a
n indefinite weight function which has several zeros and/or poles. As a bas
ic result we derive asymptotic estimates for a special fundamental system o
f solutions of the corresponding differential equation and determine the as
ymptotic distribution of the eigenvalues. Finally we prove the uniform conv
ergence of eigenfunction expansions for some class of functions f.