关于一个双次线性分数 $p$-Laplacian 方程

arXiv - MATH - Functional Analysis Pub Date : 2024-09-05 DOI:arxiv-2409.03616

A. Iannizzotto, S. Mosconi

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引用次数: 0

摘要

我们证明了由分数 $p$-Laplacian （退化或奇异）驱动的 Dirichlet 问题的分岔结果，其中反应是未知数的两个次线性幂之间的差。在我们的论证中，Sobolev vs. H\"older minima "原理发挥了根本性的作用，该原理在退化情况下已经为人所知，在此我们以更简单的证明将其扩展到奇异情况下。

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On a doubly sublinear fractional $p$-Laplacian equation

We prove a bifurcation result for a Dirichlet problem driven by the fractional $p$-Laplacian (either degenerate or singular), in which the reaction is the difference between two sublinear powers of the unknown. In our argument, a fundamental role is played by a Sobolev vs.\ H\"older minima principle, already known for the degenerate case, which here we extend to the singular case with a simpler proof.

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arXiv - MATH - Functional Analysis

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