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

Nguyen Thanh Chung; Ky Ho

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arXiv · 2006.02410

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

Nguyen Thanh Chung·Ky Ho

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Abstract

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

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Nguyen Thanh Chung, Ky Ho. 2020-06-03. On a $p(\cdot)$-biharmonic problem of Kirchhoff type involving critical growth. https://arxiv.org/abs/2006.02410

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