Uniqueness, non-degeneracy, and exact multiplicity of positive solutions for superlinear elliptic problems
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917995808292864 |
|---|---|
| author | Feltrin, Guglielmo Troestler, Christophe |
| author_facet | Feltrin, Guglielmo Troestler, Christophe |
| contents | In this paper, we focus our attention on the positive solutions to second-order nonlinear ordinary differential equations of the form $u''+q(t)g(u)=0$, where $q$ is a sign-changing weight and $g$ is a superlinear function. We exploit the classical shooting approach and the comparison theorem to present non-degeneracy and exact multiplicity results for positive solutions. This completes the multiplicity results obtained by Feltrin and Zanolin. Numerical examples and some related open problems are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05664 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniqueness, non-degeneracy, and exact multiplicity of positive solutions for superlinear elliptic problems Feltrin, Guglielmo Troestler, Christophe Analysis of PDEs 34B08, 34B15, 34B18, 34C23 In this paper, we focus our attention on the positive solutions to second-order nonlinear ordinary differential equations of the form $u''+q(t)g(u)=0$, where $q$ is a sign-changing weight and $g$ is a superlinear function. We exploit the classical shooting approach and the comparison theorem to present non-degeneracy and exact multiplicity results for positive solutions. This completes the multiplicity results obtained by Feltrin and Zanolin. Numerical examples and some related open problems are also discussed. |
| title | Uniqueness, non-degeneracy, and exact multiplicity of positive solutions for superlinear elliptic problems |
| topic | Analysis of PDEs 34B08, 34B15, 34B18, 34C23 |
| url | https://arxiv.org/abs/2405.05664 |