Spectral exactness and spectral inclusion for singular left-definite Sturm-Liouville problems
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.
scientific article; zbMATH DE number 2119248
scientific article