脉冲 Sturm-Liouville 边界值问题正解的多重性和不存在性

IF 1.7 4区数学 Q1 Mathematics

Boundary Value Problems Pub Date : 2024-04-08 DOI:10.1186/s13661-024-01840-8

Xuxin Yang, Piao Liu, Weibing Wang

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引用次数: 0

摘要

本文研究了带参数的非线性脉冲 Sturm-Liouville 边界值问题正解的存在性、不存在性和多重性。通过使用变分法，我们证明该问题在参数 $\lambda \in (0,\Lambda )$ 时至少有两个正解，在 $\lambda =\Lambda $ 时有一个正解，而在 $\lambda >\Lambda $ 时没有正解，其中 $\Lambda >0$ 是一个常数。

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Multiplicity and nonexistence of positive solutions to impulsive Sturm–Liouville boundary value problems

In this paper, we study the existence, nonexistence, and multiplicity of positive solutions to a nonlinear impulsive Sturm–Liouville boundary value problem with a parameter. By using a variational method, we prove that the problem has at least two positive solutions for the parameter $\lambda \in (0,\Lambda )$ , one positive solution for $\lambda =\Lambda $ , and no positive solution for $\lambda >\Lambda $ , where $\Lambda >0$ is a constant.

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来源期刊

Boundary Value Problems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.00

自引率

5.90%

发文量

审稿时长

4 months

期刊介绍： The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.