An Orlicz space approach to exponential elliptic problems in higher dimensions
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909545734864896 |
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| author | Boscaggin, Alberto Colasuonno, Francesca Noris, Benedetta Sani, Federica |
| author_facet | Boscaggin, Alberto Colasuonno, Francesca Noris, Benedetta Sani, Federica |
| contents | We consider semilinear elliptic problems of the form \[ -Δu + λu = f(x,u), \quad u\in H^1_0(A), \] where $A\subset\mathbb{R}^N$, $N\geq3$, is either a bounded or unbounded annulus, and $λ\geq0$. We study a broad class of nonlinearities $f$ with superlinear growth at infinity, including exponential- and power-type ones. Under suitable assumptions, we establish the existence of a positive nonradial solution via techniques in the spirit of Szulkin's nonsmooth critical point theory, applied within a convex cone in Orlicz spaces. Notably, the Trudinger-Moser inequality fails in the whole Sobolev space $H^1_0(A)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_16105 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Orlicz space approach to exponential elliptic problems in higher dimensions Boscaggin, Alberto Colasuonno, Francesca Noris, Benedetta Sani, Federica Analysis of PDEs 35J20, 35B06, 35B33 We consider semilinear elliptic problems of the form \[ -Δu + λu = f(x,u), \quad u\in H^1_0(A), \] where $A\subset\mathbb{R}^N$, $N\geq3$, is either a bounded or unbounded annulus, and $λ\geq0$. We study a broad class of nonlinearities $f$ with superlinear growth at infinity, including exponential- and power-type ones. Under suitable assumptions, we establish the existence of a positive nonradial solution via techniques in the spirit of Szulkin's nonsmooth critical point theory, applied within a convex cone in Orlicz spaces. Notably, the Trudinger-Moser inequality fails in the whole Sobolev space $H^1_0(A)$. |
| title | An Orlicz space approach to exponential elliptic problems in higher dimensions |
| topic | Analysis of PDEs 35J20, 35B06, 35B33 |
| url | https://arxiv.org/abs/2503.16105 |