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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 16
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Research Article

On a p⋅-biharmonic problem of Kirchhoff type involving critical growth

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Pages 5700-5726 | Received 18 Dec 2020, Accepted 03 Mar 2021, Published online: 22 Mar 2021
 

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.

2010 Mathematics Subject Classifications:

Acknowledgments

The second author was supported by the University of Economics Ho Chi Minh City, Vietnam.

Disclosure statement

No potential conflict of interest was reported by the author(s).

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