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A p-Laplacian problem with slightly subcritical regularly varying nonlinearity

Year: 2026

Type: article

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.

Source: Topological Methods in Nonlinear Analysis

DOI: 10.12775/tmna.2025.047

Authors: Mabel Cuesta, Rosa Pardo

Institutions: Université du littoral côte d'opale, Universidad Complutense de Madrid

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4416966532

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