A perturbation method for spinorial Yamabe type equations on and its application

For , we prove the existence of non-trivial solutions for a certain kind of nonlinear Dirac equations with critical Sobolev nonlinearities on via a perturbative variational method. For the special case , this establishes the existence of a conformal immersion with prescribed mean curvature which is...

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Bibliographic Details
Published inMathematische annalen Vol. 355; no. 4; pp. 1255 - 1299
Main Author Isobe, Takeshi
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.04.2013
Subjects
Mathematics
Mathematics and Statistics
53C42
58E05
35Q41
57R70
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ISSN0025-5831
1432-1807
DOI10.1007/s00208-012-0818-9

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Summary:For , we prove the existence of non-trivial solutions for a certain kind of nonlinear Dirac equations with critical Sobolev nonlinearities on via a perturbative variational method. For the special case , this establishes the existence of a conformal immersion with prescribed mean curvature which is close to a positive constant under an index counting condition on .
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-012-0818-9