无限图上带势能椭圆方程的柳维尔定理

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS

ACS Applied Bio Materials Pub Date : 2024-07-04 DOI:10.1007/s00526-024-02768-8

Stefano Biagi, Giulia Meglioli, Fabio Punzo

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引用次数: 0

摘要

我们研究了在无穷图上提出的一类带势函数的椭圆方程的 Liouville 特性的有效性。在对图和势作适当假设的条件下，我们证明了唯一有界解是（u\equiv 0\）。我们还证明，在一类特殊的图上，关于势的条件是最优的，即如果它失效，则存在无穷多个有界解。

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A Liouville theorem for elliptic equations with a potential on infinite graphs

We investigate the validity of the Liouville property for a class of elliptic equations with a potential, posed on infinite graphs. Under suitable assumptions on the graph and on the potential, we prove that the unique bounded solution is \(u\equiv 0\). We also show that on a special class of graphs the condition on the potential is optimal, in the sense that if it fails, then there exist infinitely many bounded solutions.

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来源期刊

ACS Applied Bio Materials Chemistry-Chemistry (all)

CiteScore

9.40

自引率

2.10%

发文量

464