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.

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.

Singularly perturbed elliptic equations with solutions concentrating on 1-dimensional orbits

B. Ruf
Primo
;
2010

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.
Superlinear ellliptic equation; singular perturbation, peaked solutions; concentrating solutions
Settore MAT/05 - Analisi Matematica
2010
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/150486
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