Singularly perturbed elliptic equations with solutions concentrating on a 1-dimensional orbit
Bernhard RufUniversità degli Studi di Milano, Italy
P.N. SrikanthT.I.F.R. Center, Bangalore, India
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. 413–427DOI 10.4171/JEMS/203