Positive Solutions to the Discrete p-Laplacian Boundary Value Problem of Kirchhoff-Type

被引：0

作者：

Chen, Zhi ^{[1
]}

Zhou, Zhan ^{[1
,2
]}

机构：

[1] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Peoples R China

[2] Guangzhou Univ, Guangzhou Ctr Appl Math, Guangzhou 510006, Peoples R China

来源：

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2025年 / 48卷 / 04期

基金：

中国国家自然科学基金;

关键词：

p-Laplacian; Boundary value problem; Positive solutions; Critical point theory; Strong maximum principle; MULTIPLE SOLUTIONS; EXISTENCE;

D O I：

10.1007/s40840-025-01899-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The objective of this paper is to investigate the existence of positive solutions to the discrete p-Laplacian boundary value problem of Kirchhoff-type by means of the critical point theory. It is demonstrated that the problem possesses at least three solutions or at least two solutions under distinct assumptions regarding the nonlinear term f. We establish a strong maximum principle for the problem and obtain the existence and multiplicity of positive solutions. When we apply our theorems to the classical problem of Kirchhoff-type, we obtain new conditions for the existence of three positive solutions. Finally, we take three examples to verify our results.

引用

页数：20

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