Singularly perturbed elliptic equations with solutions concentrating on 1-dimensional orbits
Articolo
Data di Pubblicazione:
2010
Citazione:
Singularly perturbed elliptic equations with solutions concentrating on 1-dimensional orbits / B. Ruf, P.N. Srikanth. - In: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. - ISSN 1435-9855. - 12:2(2010), pp. 413-427.
Abstract:
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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Superlinear ellliptic equation; singular perturbation, peaked solutions; concentrating solutions
Elenco autori:
B. Ruf, P.N. Srikanth
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