High perturbations of a new Kirchhoff problem involving the p-Laplace operator
Abstract In the present work we are concerned with the existence and multiplicity of solutions for the following new Kirchhoff problem involving the p-Laplace operator: { − ( a − b ∫ Ω | ∇ u | p d x ) Δ p u = λ | u | q − 2 u + g ( x , u ) , x ∈ Ω , u = 0 , x ∈ ∂ Ω , $$ \textstyle\begin{cases} - (a-b...
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
SpringerOpen
2021
|
| Materias: | |
| Acceso en línea: | https://doaj.org/article/d08db5fe8c5349c9995010f1138d6f44 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| id |
oai:doaj.org-article:d08db5fe8c5349c9995010f1138d6f44 |
|---|---|
| record_format |
dspace |
| spelling |
oai:doaj.org-article:d08db5fe8c5349c9995010f1138d6f442021-12-05T12:07:30ZHigh perturbations of a new Kirchhoff problem involving the p-Laplace operator10.1186/s13661-021-01566-x1687-2770https://doaj.org/article/d08db5fe8c5349c9995010f1138d6f442021-12-01T00:00:00Zhttps://doi.org/10.1186/s13661-021-01566-xhttps://doaj.org/toc/1687-2770Abstract In the present work we are concerned with the existence and multiplicity of solutions for the following new Kirchhoff problem involving the p-Laplace operator: { − ( a − b ∫ Ω | ∇ u | p d x ) Δ p u = λ | u | q − 2 u + g ( x , u ) , x ∈ Ω , u = 0 , x ∈ ∂ Ω , $$ \textstyle\begin{cases} - (a-b\int _{\Omega } \vert \nabla u \vert ^{p}\,dx ) \Delta _{p}u = \lambda \vert u \vert ^{q-2}u + g(x, u), & x \in \Omega , \\ u = 0, & x \in \partial \Omega , \end{cases} $$ where a , b > 0 $a, b > 0$ , Δ p u : = div ( | ∇ u | p − 2 ∇ u ) $\Delta _{p} u := \operatorname{div}(|\nabla u|^{p-2}\nabla u)$ is the p-Laplace operator, 1 < p < N $1 < p < N$ , p < q < p ∗ : = ( N p ) / ( N − p ) $p < q < p^{\ast }:=(Np)/(N-p)$ , Ω ⊂ R N $\Omega \subset \mathbb{R}^{N}$ ( N ≥ 3 $N \geq 3$ ) is a bounded smooth domain. Under suitable conditions on g, we show the existence and multiplicity of solutions in the case of high perturbations (λ large enough). The novelty of our work is the appearance of new nonlocal terms which present interesting difficulties.Zhongyi ZhangYueqiang SongSpringerOpenarticlep-Laplace operatorNew Kirchhoff problemVariational methodAnalysisQA299.6-433ENBoundary Value Problems, Vol 2021, Iss 1, Pp 1-12 (2021) |
| institution |
DOAJ |
| collection |
DOAJ |
| language |
EN |
| topic |
p-Laplace operator New Kirchhoff problem Variational method Analysis QA299.6-433 |
| spellingShingle |
p-Laplace operator New Kirchhoff problem Variational method Analysis QA299.6-433 Zhongyi Zhang Yueqiang Song High perturbations of a new Kirchhoff problem involving the p-Laplace operator |
| description |
Abstract In the present work we are concerned with the existence and multiplicity of solutions for the following new Kirchhoff problem involving the p-Laplace operator: { − ( a − b ∫ Ω | ∇ u | p d x ) Δ p u = λ | u | q − 2 u + g ( x , u ) , x ∈ Ω , u = 0 , x ∈ ∂ Ω , $$ \textstyle\begin{cases} - (a-b\int _{\Omega } \vert \nabla u \vert ^{p}\,dx ) \Delta _{p}u = \lambda \vert u \vert ^{q-2}u + g(x, u), & x \in \Omega , \\ u = 0, & x \in \partial \Omega , \end{cases} $$ where a , b > 0 $a, b > 0$ , Δ p u : = div ( | ∇ u | p − 2 ∇ u ) $\Delta _{p} u := \operatorname{div}(|\nabla u|^{p-2}\nabla u)$ is the p-Laplace operator, 1 < p < N $1 < p < N$ , p < q < p ∗ : = ( N p ) / ( N − p ) $p < q < p^{\ast }:=(Np)/(N-p)$ , Ω ⊂ R N $\Omega \subset \mathbb{R}^{N}$ ( N ≥ 3 $N \geq 3$ ) is a bounded smooth domain. Under suitable conditions on g, we show the existence and multiplicity of solutions in the case of high perturbations (λ large enough). The novelty of our work is the appearance of new nonlocal terms which present interesting difficulties. |
| format |
article |
| author |
Zhongyi Zhang Yueqiang Song |
| author_facet |
Zhongyi Zhang Yueqiang Song |
| author_sort |
Zhongyi Zhang |
| title |
High perturbations of a new Kirchhoff problem involving the p-Laplace operator |
| title_short |
High perturbations of a new Kirchhoff problem involving the p-Laplace operator |
| title_full |
High perturbations of a new Kirchhoff problem involving the p-Laplace operator |
| title_fullStr |
High perturbations of a new Kirchhoff problem involving the p-Laplace operator |
| title_full_unstemmed |
High perturbations of a new Kirchhoff problem involving the p-Laplace operator |
| title_sort |
high perturbations of a new kirchhoff problem involving the p-laplace operator |
| publisher |
SpringerOpen |
| publishDate |
2021 |
| url |
https://doaj.org/article/d08db5fe8c5349c9995010f1138d6f44 |
| work_keys_str_mv |
AT zhongyizhang highperturbationsofanewkirchhoffprobleminvolvingtheplaplaceoperator AT yueqiangsong highperturbationsofanewkirchhoffprobleminvolvingtheplaplaceoperator |
| _version_ |
1718372220671098880 |