Spectral exactness and spectral inclusion for singular left-definite Sturm-Liouville problems (Q1888677)

This paper deals with singular left-definite Sturm-Liouville problems associated with the equation \[ -(py^{\prime})^{\prime}+qy=\lambda wy\tag{1} \] on \(J=(a,b)\) and suitable boundary conditions, where \(-\infty\leq a<b\leq\infty\), \(1/p,q,w\in L^{1}_{loc}(J;\mathbb{R})\), \(p>0\), \(|w|>0\) a.e. on \(J\), and \(w\) changes sign on \(J\). The authors discuss the approximation of the discrete and continuous spectra of (1) on \(J\) with the eigenvalues of \((1)\) on truncated intervals.