Displaying similar documents to “A free boundary problem involving limiting Sobolev exponents.”

On the p-biharmonic operator with critical Sobolev exponent

Abdelouahed El Khalil, My Driss Morchid Alaoui, Abdelfattah Touzani (2014)

Applicationes Mathematicae

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We study the existence of solutions for a p-biharmonic problem with a critical Sobolev exponent and Navier boundary conditions, using variational arguments. We establish the existence of a precise interval of parameters for which our problem admits a nontrivial solution.

On the Neumann problem for an elliptic system of equations involving the critical Sobolev exponent

J. Chabrowski, Jianfu Yang (2001)

Colloquium Mathematicae

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We consider the Neumann problem for an elliptic system of two equations involving the critical Sobolev nonlinearity. Our main objective is to study the effect of the coefficient of the critical Sobolev nonlinearity on the existence and nonexistence of least energy solutions. As a by-product we obtain a new weighted Sobolev inequality.