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