Bifurcation and multiplicity results for critical fractional p‐Laplacian problems
By Kanishka Perera, Marco Squassina, Yang Yang. 2014
100 citations recorded by the source corpus.
We prove a bifurcation and multiplicity result for a critical fractional p‐Laplacian problem that is the analog of the Brézis‐Nirenberg problem for the nonlocal quasilinear case. This extends a result in the literature for the semilinear case p=2 to all p∈(1,∞) , in particular, it gives a new existence result. When p≠2 , the nonlinear operator (−Δ)ps,s∈(0,1) , has no linear eigenspaces, so our extension is nontrivial and requires a new abstract critical point theorem that is not based on linear subspaces. We prove a new abstract result based on a pseudo‐index related to the Z2 ‐cohomological index that is applicable here.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/4604f671c01e8a957e5d44825b8455d95c72d444
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In Applied Mathematics
In Computational Theory and Mathematics
Citations in the corpus
- A multiplicity results for a singular problem involving the fractional p-Laplacian operator (2016, background): “[19] with additional new abstract based on a pseudo-index related to theZ2-cohomological index.”