Bifurcation and multiplicity results for critical p-Laplacian problems
Kanishka Perera, Marco Squassina, Yang Yang
TL;DR
This paper establishes bifurcation and multiple solution results for a critical p-Laplacian problem, extending classical results to the quasilinear case independently of the spatial dimension.
Contribution
It introduces a dimension-independent bifurcation and multiplicity result for the critical p-Laplacian, generalizing the Brezis-Nirenberg problem to quasilinear equations.
Findings
Proves bifurcation points for the p-Laplacian problem.
Shows existence of multiple solutions.
Extends classical semilinear results to quasilinear cases.
Abstract
We prove a bifurcation and multiplicity result that is independent of the dimension N for a critical p-Laplacian problem that is the analog of the Brezis-Nirenberg problem for the quasilinear case. This extends a result in the literature for the semilinear case.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering · Nonlinear Differential Equations Analysis