On the asymptotic distribution of the eigenvalues of singular Sturm-Liouville problems with an indefinite weight function (Q1378899)

The asymptotic distribution of the eigenvalues of the following Sturm-Liouville problem is studied: \[ -u''+a(x)u=\rho ^2\phi ^2(x)u,\quad x\in [0,\infty); \] \[ u(0) \cos \alpha + u'(0) \sin \alpha = 0 \quad \text{ with fixed } \alpha \in [0,2\pi); \] \[ \int _0^\infty | \phi ^2| | u| ^2 < \infty , \] where \(\rho ^2\in \mathbb{C}\), \(0\leq \text{arg } \rho \leq \pi \) and the weight function \(\phi ^2\) is real-valued with a finite number of zeros.