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

Journal of the European Mathematical Society (2010)

- Volume: 012, Issue: 2, page 413-427
- ISSN: 1435-9855

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topRuf, 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 -

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