Bifurcation and multiplicity results for critical p-Laplacian problems

Kanishka Perera, Marco Squassina, Yang Yang



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 p = 2 to all p in (1;infty). In particular, it gives a new existence result when N \le p^2. When p \neq 2 the nonlinear operator -\Delta_p 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 pseudoindex related to the Z^2-cohomological index that is applicable here.


p-Laplacian; critical nonlinearity; bifurcation; multiplicity; existence; abstract critical point theory; Z^2-cohomological index; pseudo-index

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