Geodesic
Singularly perturbed elliptic equations with solutions concentrating on a 1-dimensional orbit
Journal of the European Mathematical Society, Tome 12 (2010) no. 2, pp. 413-427 Cet article a éte moissonné depuis la source EMS Press

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We consider a singularly perturbed elliptic equation with superlinear nonlinearity on an annulus in R4, and look for solutions which are invariant under a fixed point free 1-parameter group action. We show that this problem can be reduced to a nonhomogeneous equation on a related annulus in dimension 3. The ground state solutions of this equation are single peak solutions which concentrate near the inner boundary. Transforming back, these solutions produce a family of solutions which concentrate along the orbit of the group action near the inner boundary of the domain.
DOI : 10.4171/jems/203
Classification : 35-XX, 00-XX
Keywords: Superlinear ellliptic equation, singular perturbation, peaked solutions, concentrating solutions 
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     author = {Bernhard Ruf and P.N. Srikanth},
     title = {Singularly perturbed elliptic equations with solutions concentrating on a 1-dimensional orbit},
     journal = {Journal of the European Mathematical Society},
     pages = {413--427},
     year = {2010},
     volume = {12},
     number = {2},
     doi = {10.4171/jems/203},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/203/}
}
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Bernhard Ruf; P.N. Srikanth. Singularly perturbed elliptic equations with solutions concentrating on a 1-dimensional orbit. Journal of the European Mathematical Society, Tome 12 (2010) no. 2, pp. 413-427. doi: 10.4171/jems/203

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