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

被引：0

作者：

Pandey, Prashant K. ^{[1
]}

Pandey, Rajesh K. ^{[1
]}

Agrawal, Om P. ^{[2
]}

机构：

[1] Indian Inst Technol BHU Varanasi, Dept Math Sci, Varanasi 221005, UP, India

[2] Southern Illinois Univ, Mech Engn & Energy Proc, Carbondale, IL 62901 USA

来源：

MATHEMATICAL COMMUNICATIONS | 2023年 / 28卷 / 01期

关键词：

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

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：141 / 152

页数：12

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