Positive Solutions for Third-Order Boundary Value Problems with Indefinite Weight

被引：1

作者：

Bi, Zhonghua ^{[1
]}

Liu, Sanyang ^{[1
]}

机构：

[1] Xidian Univ, Sch Math & Stat, Xian 710126, Peoples R China

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2023年 / 20卷 / 06期

关键词：

Disconjugacy; eigenvalues; indefinite weight; third-order boundary-value problem; bifurcation; EXISTENCE;

D O I：

10.1007/s00009-023-02507-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we initially employ the disconjugacy theory to establish some sufficient conditions for the disconjugacy of y''' + beta y '' + alpha y' = 0. We then utilize Elias's spectrum theory to demonstrate the spectrum structure of the linear operator y''' + beta y '' + alpha y' coupled with the boundary conditions y(0) = y(1) = y' (1) = 0. Ultimately, by utilizing the acquired results, we ascertain the existence of positive solutions for the corresponding nonlinear third-order problem with an indefinite weight, based on the principles of bifurcation theory and the Leray-Schauder fixed point theorem.

引用

页数：18

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