Note on elliptic equations on closed manifolds with singular nonlinearities
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913812954742784 |
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| author | Bieganowski, Bartosz Konysz, Adam |
| author_facet | Bieganowski, Bartosz Konysz, Adam |
| contents | We consider a general elliptic equation $$ -Δ_g u+V(x)u=f(x,u)+g(x,u^2)u $$ on a closed Riemannian manifold $(M, g)$ and utilize a recent variational approach by Hebey, Pacard, Pollack to show the existence of a nontrivial solution under general assumptions on nonlinear terms $f$ and $g$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21339 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Note on elliptic equations on closed manifolds with singular nonlinearities Bieganowski, Bartosz Konysz, Adam Analysis of PDEs 35Q75, 35A15, 35J20, 58J05, 83C05 We consider a general elliptic equation $$ -Δ_g u+V(x)u=f(x,u)+g(x,u^2)u $$ on a closed Riemannian manifold $(M, g)$ and utilize a recent variational approach by Hebey, Pacard, Pollack to show the existence of a nontrivial solution under general assumptions on nonlinear terms $f$ and $g$. |
| title | Note on elliptic equations on closed manifolds with singular nonlinearities |
| topic | Analysis of PDEs 35Q75, 35A15, 35J20, 58J05, 83C05 |
| url | https://arxiv.org/abs/2504.21339 |