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

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

[学科分类] 工程和技术（综合）

[关键词] Generalized derivative;Generalized Sturm-comparison theorem;generalized Sturm--Liouville problem