A note on critical problems involving the $p$-Grushin Operator: existence of infinitely many solutions

Paolo Malanchini; Giovanni Molica Bisci; Simone Secchi

doi:10.48550/arxiv.2601.09488

A note on critical problems involving the $p$-Grushin Operator: existence of infinitely many solutions

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Paolo Malanchini, Giovanni Molica Bisci, Simone Secchi

DOI: 10.48550/arxiv.2601.09488

Cited by: 0

Abstract

We consider a critical problem in a bounded domain involving the $p$-Grushin operator $Δ_α^p$. After a truncation argument, we obtain infinitely many solutions to our problem via Krasnoselskii's genus, extending a previous result of García Azorero and Peral Alonso to the $p$-Grushin operator. A central part of our analysis is the verification of the Palais-Smale condition of the associated functional under a certain level.

Fields of Study & Subjects

Nonlinear Partial Differential Equations Nonlinear Differential Equations Analysis Geometric Analysis and Curvature Flows

Publication details

Journal / source: arXiv (Cornell University)
Publication date: 14 January 2026
Document type: Preprint