JournalsjemsVol. 12, No. 2pp. 413–427

Singularly perturbed elliptic equations with solutions concentrating on a 1-dimensional orbit

  • Bernhard Ruf

    Università degli Studi di Milano, Italy
  • P.N. Srikanth

    T.I.F.R. Center, Bangalore, India
Singularly perturbed elliptic equations with solutions concentrating on a 1-dimensional orbit cover
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Abstract

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.

Cite this article

Bernhard Ruf, P.N. Srikanth, Singularly perturbed elliptic equations with solutions concentrating on a 1-dimensional orbit. J. Eur. Math. Soc. 12 (2010), no. 2, pp. 413–427

DOI 10.4171/JEMS/203