arXiv:2006.02410 Abstract | arXiv Analytics

arXiv:2006.02410 [math.AP]Abstract References Reviews Resources

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

Published 2020-06-03Version 1

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.

Categories: math.AP

Subjects: 35B33, 35J20, 35J60, 35G30, 46E35, 49J35

Keywords: critical growth, biharmonic problem, kirchhoff type problems, sobolev space, biharmonic operator

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