We obtain nontrivial solutions of a critical (p, q)-Laplacian problem in a bounded domain. In addition to the usual difficulty of the loss of compactness associated with problems involving critical Sobolev exponents, this problem lacks a direct sum decomposition suitable for applying the classical linking theorem. We show that every Palais–Smale sequence at a level below a certain energy threshold admits a subsequence that converges weakly to a nontrivial critical point of the variational functional. Then we prove an abstract critical point theorem based on a cohomological index and use it to construct a minimax level below this threshold.
Candito, P., Marano, S.A., Perera, K. (2015). On a class of critical (p, q)-Laplacian problems. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 22(6), 1959-1972 [10.1007/s00030-015-0353-y].
On a class of critical (p, q)-Laplacian problems
Candito, Pasquale;
2015-01-01
Abstract
We obtain nontrivial solutions of a critical (p, q)-Laplacian problem in a bounded domain. In addition to the usual difficulty of the loss of compactness associated with problems involving critical Sobolev exponents, this problem lacks a direct sum decomposition suitable for applying the classical linking theorem. We show that every Palais–Smale sequence at a level below a certain energy threshold admits a subsequence that converges weakly to a nontrivial critical point of the variational functional. Then we prove an abstract critical point theorem based on a cohomological index and use it to construct a minimax level below this threshold.File | Dimensione | Formato | |
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