Paolo Malanchini, Giovanni Molica Bisci, Simone Secchi
Abstract:
We consider a critical problem in a bounded domain involving the p-Grushin operator.
After a truncation argument, we obtain infinitely many solutions to our problem via Krasnoselskii's genus, extending a previous result of Garcia Azorero and Peral Alonso in [13] 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.
Submitted February 2, 2026. Published August 10, 2026.
Math Subject Classifications: 35J70, 35B33, 35J20.
Key Words: p-Grushin operator; critical exponent; genus.
DOI: 10.58997/ejde.2026.59
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Paolo Malanchini Dipartimento di Matematica e Applicazioni Università degli Studi di Milano Bicocca, via Roberto Cozzi 55, 20125, Milano, Italy email: p.malanchini@campus.unimib.it |
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Giovanni Molica Bisci Department of Human Sciences and Promotion of Quality of Life San Raffaele University via di Val Cannuta 247, I-00166 Roma, Italy email: giovanni.molicabisci@uniroma5.it |
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Simone Secchi Dipartimento di Matematica e Applicazioni Università degli Studi di Milano Bicocca, via Roberto Cozzi 55, 20125, Milano, Italy email: simone.secchi@unimib.it |
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