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- W2079173824 abstract "Given (M,g) a smooth compact Riemannian manifold of dimension n ≥ 5, we consider equations like $$P_{g} u = u^{{2^{# } - 1}} ,$$ where $$P_{g} u = Delta ^{2}_{g} u + alpha Delta _{g} u + a_{alpha } u$$ is a Paneitz-Branson type operator with constant coefficients α and aα, u is required to be positive, and $$2^{# } = frac{{2n}}{{n - 4}}$$ is critical from the Sobolev viewpoint. We define the energy function E m as the infimum of $$E{left( u right)} = ||u||^{{2^{# } }}_{{2^{# } }} $$ over the u’s which are solutions of the above equation. We prove that E m (α ) →+∞ as α →+∞ . In particular, for any Λ > 0, there exists α0 > 0 such that for α ≥ α0, the above equation does not have a solution of energy less than or equal to Λ." @default.
- W2079173824 created "2016-06-24" @default.
- W2079173824 creator A5068978273 @default.
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- W2079173824 date "2005-08-01" @default.
- W2079173824 modified "2023-10-17" @default.
- W2079173824 title "Fourth order equations of critical Sobolev growth. Energy function and solutions of bounded energy in the conformally flat case" @default.
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- W2079173824 doi "https://doi.org/10.1007/s00030-005-0011-x" @default.
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