On a <i>p</i>⋅-biharmonic problem of Kirchhoff type involving critical growth

Abstract

We establish a concentration-compactness principle for the Sobolev space W2,p(⋅)(Ω)∩W01,p(⋅)(Ω) that is a tool for overcoming the lack of compactness of the critical Sobolev imbedding. Using this result, we obtain several existence and multiplicity results for a class of Kirchhoff type problems involving p(⋅)-biharmonic operator and critical growth.