Nonlinear Dirac equations with critical nonlinearities on compact spin manifolds (Q610757)
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scientific article; zbMATH DE number 5825482
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nonlinear Dirac equations with critical nonlinearities on compact spin manifolds |
scientific article; zbMATH DE number 5825482 |
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Nonlinear Dirac equations with critical nonlinearities on compact spin manifolds (English)
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10 December 2010
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The main result of this paper is the existence of a non trivial solution to a semilinear elliptic equation associated to the Dirac operator on a compact manifold of dimension at least 4 and with critical power nonlinearity. It is a Dirac analogue of the Brezis-Nirenberg problem in that it involves a linear term depending on a real spectral parameter which belongs to the resolvent set of the (Dirac) operator. This result generalizes a previous one by Ammann.
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nonlinear Dirac equations
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critical Sobolev exponent
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strongly indefinite functional
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critical point theory
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compactness
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regularity
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