Non-real eigenvalues of symmetric Sturm–Liouville problems with indefinite weight functions

The present paper deals with non-real eigenvalues of regular Sturm–Liouville problems with odd symmetry indefinite weight functions applying the two-parameter method. Sufficient conditions for the existence and non-existence of non-real eigenvalues are obtained. Furthermore, an explicit expression of the bound of non-real eigenvalues will be given in the paper.