Configuration spaces and multiple positive solutions to a singularly perturbed elliptic system
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913180902490112 |
|---|---|
| author | Clapp, Mónica Saldaña, Alberto Szulkin, Andrzej |
| author_facet | Clapp, Mónica Saldaña, Alberto Szulkin, Andrzej |
| contents | We consider a weakly coupled singularly perturbed variational elliptic system in a bounded smooth domain with Dirichlet boundary conditions. We show that, in the competitive regime, the number of fully nontrivial solutions with nonnegative components increases with the number of equations. Our proofs use a combination of four key elements: a convenient variational approach, the asymptotic behavior of solutions (concentration), the Lusternik-Schnirelman theory, and new estimates on the category of suitable configuration spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_12580 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Configuration spaces and multiple positive solutions to a singularly perturbed elliptic system Clapp, Mónica Saldaña, Alberto Szulkin, Andrzej Analysis of PDEs 35J50, 35B06, 35B40, 35B09, 35B25, 55M30, 55R80 We consider a weakly coupled singularly perturbed variational elliptic system in a bounded smooth domain with Dirichlet boundary conditions. We show that, in the competitive regime, the number of fully nontrivial solutions with nonnegative components increases with the number of equations. Our proofs use a combination of four key elements: a convenient variational approach, the asymptotic behavior of solutions (concentration), the Lusternik-Schnirelman theory, and new estimates on the category of suitable configuration spaces. |
| title | Configuration spaces and multiple positive solutions to a singularly perturbed elliptic system |
| topic | Analysis of PDEs 35J50, 35B06, 35B40, 35B09, 35B25, 55M30, 55R80 |
| url | https://arxiv.org/abs/2306.12580 |