Singular left-definite Sturm–Liouville problems

We study singular left-definite Sturm–Liouville problems with an indefinite weight function. The existence of eigenvalues is established based on the existence of eigenvalues of corresponding rightdefinite problems. Furthermore, for each singular left-definite problem with limit-circle nonoscillatory endpoints we construct a regular leftdefinite problem with the same eigenvalues and use it to obtain properties of eigenvalues and eigenfunctions. Inequalities among eigenvalues recently established for regular left-definite problems are extended to the singular case.