Multiple solutions for a class of nonhomogeneous elliptic systems with Dirichlet boundary or Neumann boundary
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911935089344512 |
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| author | Yu, Xiaoli Zhang, Xingyong |
| author_facet | Yu, Xiaoli Zhang, Xingyong |
| contents | In this paper, we mainly establish the existence of at least three non-trivial solutions for a class of nonhomogeneous quasilinear elliptic systems with Dirichlet boundary value or Neumann boundary value in a bounded domain $Ω\subset\mathbb{R}^N $ and $N\geq 1$. We exploit the method which is based on [6]. This method let us obtain the concrete open interval about the parameter $λ$. Since the quasilinear term depends on $u$ and $\nabla u$, it is necessary for our proofs to use the theory of monotone operators and the skill of adding one dimension to space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19027 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multiple solutions for a class of nonhomogeneous elliptic systems with Dirichlet boundary or Neumann boundary Yu, Xiaoli Zhang, Xingyong Analysis of PDEs In this paper, we mainly establish the existence of at least three non-trivial solutions for a class of nonhomogeneous quasilinear elliptic systems with Dirichlet boundary value or Neumann boundary value in a bounded domain $Ω\subset\mathbb{R}^N $ and $N\geq 1$. We exploit the method which is based on [6]. This method let us obtain the concrete open interval about the parameter $λ$. Since the quasilinear term depends on $u$ and $\nabla u$, it is necessary for our proofs to use the theory of monotone operators and the skill of adding one dimension to space. |
| title | Multiple solutions for a class of nonhomogeneous elliptic systems with Dirichlet boundary or Neumann boundary |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.19027 |