Multiplicity of positive solutions to semi-linear elliptic problems on metric graphs (Q2062559)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Multiplicity of positive solutions to semi-linear elliptic problems on metric graphs |
scientific article; zbMATH DE number 7451060
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Multiplicity of positive solutions to semi-linear elliptic problems on metric graphs |
scientific article; zbMATH DE number 7451060 |
Statements
Multiplicity of positive solutions to semi-linear elliptic problems on metric graphs (English)
0 references
27 December 2021
0 references
Let \(\varepsilon\) be a positive suffciently small parameter and \(p>1\). The author considers positive solutions of the semi-linear elliptic equation \(-\varepsilon^2 u''+ u = u^p\) on a compact metric graph \(G\). Neumann or Dirichlet boundary conditions are given on the ends of \(G\). The author establishes the existence of the positive solution concentrated on an edge (single-peak solution).
0 references
metric graph
0 references
variational method
0 references
Nehari manifold
0 references
positive solution
0 references
multiplicity
0 references
0 references
0 references
0 references
0.93017775
0 references
0.9243742
0 references
0.91405123
0 references
0.91349316
0 references
0.91310644
0 references
0.9129043
0 references
