Entire Nodal Solutions with Prescribed Symmetry to Caffarelli-Kohn-Nirenberg Equations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917080356356096 |
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| author | Chernysh, Edward |
| author_facet | Chernysh, Edward |
| contents | We establish the existence of sign-changing entire solutions to weighted critical $p$-Laplace equations of the Caffarelli-Kohn-Nirenberg type. In doing so, we investigate classes of symmetry and show that, for suitable symmetry configurations, there exists a non-trivial solution which changes sign and respects the corresponding prescribed symmetry. In addition, we describe conditions under which these symmetry-types are incompatible. Especially, we demonstrate the existence of entire nodal solutions for an infinite number of distinct symmetry types. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11543 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Entire Nodal Solutions with Prescribed Symmetry to Caffarelli-Kohn-Nirenberg Equations Chernysh, Edward Analysis of PDEs 35J92 (Primary) 35B08, 35B33, 35J60 (Secondary) We establish the existence of sign-changing entire solutions to weighted critical $p$-Laplace equations of the Caffarelli-Kohn-Nirenberg type. In doing so, we investigate classes of symmetry and show that, for suitable symmetry configurations, there exists a non-trivial solution which changes sign and respects the corresponding prescribed symmetry. In addition, we describe conditions under which these symmetry-types are incompatible. Especially, we demonstrate the existence of entire nodal solutions for an infinite number of distinct symmetry types. |
| title | Entire Nodal Solutions with Prescribed Symmetry to Caffarelli-Kohn-Nirenberg Equations |
| topic | Analysis of PDEs 35J92 (Primary) 35B08, 35B33, 35J60 (Secondary) |
| url | https://arxiv.org/abs/2511.11543 |