Bifurcation and multiplicity results for critical p-Laplacian problems
DOI:
https://doi.org/10.12775/TMNA.2015.093Słowa kluczowe
p-Laplacian, critical nonlinearity, bifurcation, multiplicity, existence, abstract critical point theory, Z^2-cohomological index, pseudo-indexAbstrakt
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.Bibliografia
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