Higher-order evolution inequalities with Hardy potential on the Korányi ball
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916132269588480 |
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| author | Jleli, Mohamed Ruzhansky, Michael Samet, Bessem Torebek, Berikbol T. |
| author_facet | Jleli, Mohamed Ruzhansky, Michael Samet, Bessem Torebek, Berikbol T. |
| contents | We consider a higher order in (time) semilinear evolution inequality posed on the Korányi ball under an inhomogeneous Dirichlet-type boundary condition. The problem involves an inverse-square potential $λ/|ξ|_\mathbb{H}^2$, where $λ\geq -(Q-2)^2/4$ and a general weight function $V$ depending on the space variable in front of the power nonlinearity. We first establish a general nonexistence result for the considered problem. Next, in the special case $V(ξ):=|ξ|_\mathbb{H}^a$, $a\in \mathbb{R}$, we prove the sharpness of our nonexistence result and show that the problem admits three different critical behaviors according to the value of the parameter $λ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13158 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher-order evolution inequalities with Hardy potential on the Korányi ball Jleli, Mohamed Ruzhansky, Michael Samet, Bessem Torebek, Berikbol T. Analysis of PDEs We consider a higher order in (time) semilinear evolution inequality posed on the Korányi ball under an inhomogeneous Dirichlet-type boundary condition. The problem involves an inverse-square potential $λ/|ξ|_\mathbb{H}^2$, where $λ\geq -(Q-2)^2/4$ and a general weight function $V$ depending on the space variable in front of the power nonlinearity. We first establish a general nonexistence result for the considered problem. Next, in the special case $V(ξ):=|ξ|_\mathbb{H}^a$, $a\in \mathbb{R}$, we prove the sharpness of our nonexistence result and show that the problem admits three different critical behaviors according to the value of the parameter $λ$. |
| title | Higher-order evolution inequalities with Hardy potential on the Korányi ball |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.13158 |