Supercritical Lane-Emden equation on a cone with an inhomogeneous Dirichlet boundary condition
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929600403079168 |
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| author | Katayama, Sho |
| author_facet | Katayama, Sho |
| contents | We consider the Lane-Emden equation with a supercritical nonlinearity with an inhomogeneous Dirichlet boundary condition on an infinite cone. Under suitable conditions for the boundary data and the exponent of nonlinearity, we give a complete classification of the existence/nonexistence of a solution with respect to the size of boundary data. Moreover, we give a result on the multiple existence of solutions via bifurcation theory. We also state results on Hardy-Hénon equations on infinite cones as a generalization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14686 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Supercritical Lane-Emden equation on a cone with an inhomogeneous Dirichlet boundary condition Katayama, Sho Analysis of PDEs 35J25, 35J61, 35B09, 35B32 We consider the Lane-Emden equation with a supercritical nonlinearity with an inhomogeneous Dirichlet boundary condition on an infinite cone. Under suitable conditions for the boundary data and the exponent of nonlinearity, we give a complete classification of the existence/nonexistence of a solution with respect to the size of boundary data. Moreover, we give a result on the multiple existence of solutions via bifurcation theory. We also state results on Hardy-Hénon equations on infinite cones as a generalization. |
| title | Supercritical Lane-Emden equation on a cone with an inhomogeneous Dirichlet boundary condition |
| topic | Analysis of PDEs 35J25, 35J61, 35B09, 35B32 |
| url | https://arxiv.org/abs/2411.14686 |