Global existence and multiplicity of positive solutions for anisotropic eigenvalue problems

IF 0.9 3区数学 Q2 MATHEMATICS

Mathematica Slovaca Pub Date : 2024-07-01 DOI:10.1515/ms-2024-0051

Zhenhai Liu, Nikolaos S. Papageorgiou

引用次数: 0

Abstract

We consider an eigenvalue problem driven by the anisotropic (p, q)-Laplacian and with a Carathéodory reaction which is (p(z) − 1)-sublinear as x → + ∞. We look for positive solutions. We prove an existence, nonexistence and multiplicity theorem which is global in the parameter λ > 0, that is, we prove a bifurcation-type theorem which describes in an exact way the changes in the set of positive solutions as the parameter λ varies on ℝ̊+ = (0, + ∞).

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各向异性特征值问题正解的全局存在性和多重性

我们考虑一个由各向异性（p, q）-拉普拉奇驱动的特征值问题，它具有 Carathéodory 反应，在 x → + ∞ 时为 (p(z) - 1)-次线性。我们寻找正解。我们证明了一个存在、不存在和多重性定理，它在参数 λ > 0 中是全局的，也就是说，我们证明了一个分岔型定理，它以精确的方式描述了参数 λ 在 ℝ̊+ = (0, + ∞) 上变化时正解集的变化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematica Slovaca 数学-数学

CiteScore

2.10

自引率

6.20%

发文量

审稿时长

6-12 weeks

期刊介绍： Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process. Its reputation was approved by many outstanding mathematicians who already contributed to Math. Slovaca. It makes bridges among mathematics, physics, soft computing, cryptography, biology, economy, measuring, etc.　 The Journal publishes original articles with complete proofs. Besides short notes the journal publishes also surveys as well as some issues are focusing on a theme of current interest.