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arXiv · 2610.38596

A $p$-Laplacian Problem with Slightly Subcritical Regularly Varying Nonlinearity

Mabel Cuesta·Rosa Pardo
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Abstract

We study a quasilinear elliptic problem involving the $p$-laplacian operator and a slightly subcritical nonlinearity with a sign-changing weight. We assume that the slightly subcritical nonlinearity is a regularly varying function at zero and at infinity, which are not necessarily asymptotic to a power at infinity. We state sufficient conditions which guarantee a Palais-Smale condition. We also provide a bifurcation theorem for these nonlinearities, which allow us to state the existence of a bifurcated branch of positive solutions, containing a turning point, and multiplicity of solutions.

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Mabel Cuesta, Rosa Pardo. 2026-10-28. A $p$-Laplacian Problem with Slightly Subcritical Regularly Varying Nonlinearity. https://doi.org/10.12775/tmna.2025.047

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