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arXiv · 2603.20095

An eigenvalue problem for a nonlocal quasilinear anisotropic equation in fractional Orlicz Sobolev spaces without the $\Delta_2$--condition

Julian Fernandez Bonder·Martin Guzman·Juan F. Spedaletti
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Abstract

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 $\Delta_2$--condition on the Young functions involved. We show existence of a sequence of eigenpairs $(u_k,\lambda_k)\to (0,+\infty)$.

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Julian Fernandez Bonder, Martin Guzman, Juan F. Spedaletti. 2026-03-20. An eigenvalue problem for a nonlocal quasilinear anisotropic equation in fractional Orlicz Sobolev spaces without the $\Delta_2$--condition. https://arxiv.org/abs/2603.20095

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