An eigenvalue problem for a nonlocal quasilinear anisotropic equation in fractional Orlicz Sobolev spaces without the $Δ_2$--condition
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914418635309056 |
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| author | Bonder, Julian Fernandez Guzman, Martin Spedaletti, Juan F. |
| author_facet | Bonder, Julian Fernandez Guzman, Martin Spedaletti, Juan F. |
| contents | In this paper we analyze an eigenvalue problem associated to fractional operators of the form \[ L_a^s u(x)=2 \text{p.v.}\int_{\mathbb{R}^n}a(x,y,D^su(x,y))\,\frac{dy}{|x-y|^{n+s}},\] which represents a generalization model for nonlocal, nonstandard growth diffusion problems. We study this problem in the context of the fractional Orlicz Sobolev spaces without assuming the so-called $Δ_2$--condition on the Young functions involved. We show existence of a sequence of eigenpairs $(u_k,λ_k)\to (0,+\infty)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20095 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An eigenvalue problem for a nonlocal quasilinear anisotropic equation in fractional Orlicz Sobolev spaces without the $Δ_2$--condition Bonder, Julian Fernandez Guzman, Martin Spedaletti, Juan F. Analysis of PDEs 35J62, 35P30, 46E30 In this paper we analyze an eigenvalue problem associated to fractional operators of the form \[ L_a^s u(x)=2 \text{p.v.}\int_{\mathbb{R}^n}a(x,y,D^su(x,y))\,\frac{dy}{|x-y|^{n+s}},\] which represents a generalization model for nonlocal, nonstandard growth diffusion problems. We study this problem in the context of the fractional Orlicz Sobolev spaces without assuming the so-called $Δ_2$--condition on the Young functions involved. We show existence of a sequence of eigenpairs $(u_k,λ_k)\to (0,+\infty)$. |
| title | An eigenvalue problem for a nonlocal quasilinear anisotropic equation in fractional Orlicz Sobolev spaces without the $Δ_2$--condition |
| topic | Analysis of PDEs 35J62, 35P30, 46E30 |
| url | https://arxiv.org/abs/2603.20095 |