Original scientific paper

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

Rajesh K Pandey ; Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, UP India
Prashnat K Pandey, ; Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, UP India
Om P Agrawal ; Mechanical Engineering and Energy Processes, Southern Illinois University, Carbondale, Illinois, USA

Abstract

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.

Keywords

Generalized derivative; Generalized Sturm-comparison theorem; generalized Sturm--Liouville problem

Hrčak ID:

303393

URI

https://hrcak.srce.hr/303393

Publication date:

2.6.2023.

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