English

On a $p(\cdot)$-biharmonic problem of Kirchhoff type involving critical growth

Analysis of PDEs 2020-06-04 v1

Abstract

We establish a concentration-compactness principle for the Sobolev space W2,p()(Ω)W01,p()(Ω)W^{2,p(\cdot)}(\Omega)\cap W_0^{1,p(\cdot)}(\Omega) 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()p(\cdot)-biharmonic operator and critical growth.

Keywords

Cite

@article{arxiv.2006.02410,
  title  = {On a $p(\cdot)$-biharmonic problem of Kirchhoff type involving critical growth},
  author = {Nguyen Thanh Chung and Ky Ho},
  journal= {arXiv preprint arXiv:2006.02410},
  year   = {2020}
}