| Abstract: |
| We obtain nontrivial solutions to the Brezis-Nirenberg problem for the fractional p-Laplacian operator, extending some results in the literature for the fractional Laplacian. The quasilinear case presents two serious new difficulties. First an explicit formula
for a minimizer in the fractional Sobolev inequality is not available when p \not= 2. We get
around this difficulty by working with certain asymptotic estimates for minimizers. The second difficulty is the lack of a direct sum decomposition suitable for
applying the classical linking theorem. We use an abstract linking theorem based on the
cohomological index to overcome this difficulty. |
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