We consider a singularly perturbed elliptic equation with superlinear nonlinearity on an annulus in R^4, 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 non-homogeneous equation on a related annulus in dimension R^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.
Singularly perturbed elliptic equations with solutions concentrating on 1-dimensional orbits / B. Ruf, P.N. Srikanth. - In: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. - ISSN 1435-9855. - 12:2(2010), pp. 413-427.
Singularly perturbed elliptic equations with solutions concentrating on 1-dimensional orbits
B. RufPrimo
;
2010
Abstract
We consider a singularly perturbed elliptic equation with superlinear nonlinearity on an annulus in R^4, 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 non-homogeneous equation on a related annulus in dimension R^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.Pubblicazioni consigliate
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