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.
|Titolo:||Singularly perturbed elliptic equations with solutions concentrating on 1-dimensional orbits|
RUF, BERNHARD (Primo)
|Parole Chiave:||Superlinear ellliptic equation; singular perturbation, peaked solutions; concentrating solutions|
|Settore Scientifico Disciplinare:||Settore MAT/05 - Analisi Matematica|
|Data di pubblicazione:||2010|
|Digital Object Identifier (DOI):||10.4171/JEMS/203|
|Appare nelle tipologie:||01 - Articolo su periodico|