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

Abstract

The present paper defines the Sturm separation and Sturm comparison theorems 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. © 2023 Department of Mathematics, University of Osijek.