Work

Bifurcation and multiplicity results for critical problems involving the p -Grushin operator

Year: 2025

Type: article

Abstract: In this article, we prove a bifurcation and multiplicity result for a critical problem involving a degenerate nonlinear operator Δ γ p {\Delta }_{\gamma }^{p} . We extend to a generic p > 1 p\gt 1 a result, which was proved only when p = 2 p=2 . When p ≠ 2 p\ne 2 , the nonlinear operator − Δ γ p -{\Delta }_{\gamma }^{p} has no linear eigenspaces, so our extension is nontrivial and requires an abstract critical theorem, which is not based on linear subspaces. We use an abstract result based on a pseudo-index related to the Z 2 {{\mathbb{Z}}}_{2} -cohomological index that is applicable here. We provide a version of the Lions’ concentration-compactness principle for our operator.

Source: Advances in Nonlinear Analysis

DOI: 10.1515/anona-2025-0089

Authors: Paolo Malanchini, Giovanni Molica Bisci, Simone Secchi

Institutions: University of Milano-Bicocca, San Raffaele University of Rome

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,469

Funder: European Commission