| Abstract: |
| In this work, we study the existence of weak solution to the following quasi linear elliptic problem involving the fractional $p$-Laplacian operator, a Hardy potential and multiple critical Sobolev nonlinearities with singularities.
To prove the existence of solution to the problem we have to formulate a refined version of the concentration-compactness principle and, as an independent result, we have to show that the extremals for the Sobolev inequality are attained. A nonexistence result is established via Pohazaev type identity. |
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