Sturm's theorems for generalized derivative and generalized Sturm-Liouville problem

The present paper defines the Sturm separation and Sturm comparison theo-rems for the generalized derivative. The generalized derivative is defined with respect to the weight function and another function. Further, we define the generalized Sturm-Liouville problem (GSLP) and analyze the properties of the GSLP such that the eigenvalues of the GSLP are real, and for distinct eigenvalues, the associated eigenfunctions are orthogonal. Moreover, using a variational approach, we show that the GSLP has infinite eigenvalues.