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

Ruf, Bernhard, and Srikanth, P.N.. "Singularly perturbed elliptic equations with solutions concentrating on a 1-dimensional orbit." Journal of the European Mathematical Society 012.2 (2010): 413-427. <http://eudml.org/doc/277379>.

@article{Ruf2010,
abstract = {We consider a singularly perturbed elliptic equation with superlinear nonlinearity on an annulus in $\mathbb \{R\}^4$, 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 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.},
author = {Ruf, Bernhard, Srikanth, P.N.},
journal = {Journal of the European Mathematical Society},
keywords = {superlinear ellliptic equation; singular perturbation; peaked solutions; concentrating solutions; superlinear ellliptic equation; singular perturbation; peaked solutions; concentrating solutions},
language = {eng},
number = {2},
pages = {413-427},
publisher = {European Mathematical Society Publishing House},
title = {Singularly perturbed elliptic equations with solutions concentrating on a 1-dimensional orbit},
url = {http://eudml.org/doc/277379},
volume = {012},
year = {2010},
}

TY - JOUR
AU - Ruf, Bernhard
AU - Srikanth, P.N.
TI - Singularly perturbed elliptic equations with solutions concentrating on a 1-dimensional orbit
JO - Journal of the European Mathematical Society
PY - 2010
PB - European Mathematical Society Publishing House
VL - 012
IS - 2
SP - 413
EP - 427
AB - We consider a singularly perturbed elliptic equation with superlinear nonlinearity on an annulus in $\mathbb {R}^4$, 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 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.
LA - eng
KW - superlinear ellliptic equation; singular perturbation; peaked solutions; concentrating solutions; superlinear ellliptic equation; singular perturbation; peaked solutions; concentrating solutions
UR - http://eudml.org/doc/277379
ER -