THE BREZIS-NIRENBERG PROBLEM FOR THE FRACTIONAL p-LAPLACIAN
نویسندگان
چکیده
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 6= 2. We get around this difficulty by working with certain asymptotic estimates for minimizers recently obtained in [4]. 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 proved in [48] to overcome this difficulty.
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