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arXiv · 2512.21959

Nonlocal Dirichlet problems involving the Logarithmic $p$-Laplacian

Rakesh Arora·Hichem Hajaiej·Kanishka Perera
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Abstract

In this work, we show the existence of an unbounded sequence of minimax eigenvalues for the logarithmic $p$-Laplacian via the $\mathbb{Z}_2$-cohomological index of Fadell and Rabinowitz. As an application of these minimax eigenvalues and $p$-logarithmic Sobolev inequality proved in [4], we prove new existence results for nonlocal Dirichlet problems involving logarithmic $p$-Laplacian and nonlinearities with $p$-superlinear and subcritical growth at infinity.

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Rakesh Arora, Hichem Hajaiej, Kanishka Perera. 2025-12-26. Nonlocal Dirichlet problems involving the Logarithmic $p$-Laplacian. https://arxiv.org/abs/2512.21959

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