Costruzione di spike-layers multidimensionali

Andrea Malchiodi

Bollettino dell'Unione Matematica Italiana (2005)

  • Volume: 8-B, Issue: 3, page 615-628
  • ISSN: 0392-4041

Abstract

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We study positive solutions of the equation - ϵ 2 ⁢ Δ ⁢ u + u = u p in Ω , where Ω ⊆ R n , p > 1 and ϵ is a positive small parameter. Usually we put Neumann boundary conditions. When ϵ goes to zero, we prove the existence of solutions which concentrate on curves or varietis.

How to cite

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Malchiodi, Andrea. "Costruzione di spike-layers multidimensionali." Bollettino dell'Unione Matematica Italiana 8-B.3 (2005): 615-628. <http://eudml.org/doc/195387>.

@article{Malchiodi2005,
abstract = {Si studiano soluzioni positive dell’equazione $-\epsilon^\{2\} \Delta u+u=u^p$ in $\Omega$, dove $\Omega\subseteq \mathbb\{R\}^\{n\}$ , $p > 1$ ed $\epsilon$ è un piccolo parametro positivo. Si impongono in genere condizioni al bordo di Neumann. Quando $\epsilon$ tende a zero, dimostriamo esistenza di soluzioni che si concentrano su curve o varietà.},
author = {Malchiodi, Andrea},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {ita},
month = {10},
number = {3},
pages = {615-628},
publisher = {Unione Matematica Italiana},
title = {Costruzione di spike-layers multidimensionali},
url = {http://eudml.org/doc/195387},
volume = {8-B},
year = {2005},
}

TY - JOUR
AU - Malchiodi, Andrea
TI - Costruzione di spike-layers multidimensionali
JO - Bollettino dell'Unione Matematica Italiana
DA - 2005/10//
PB - Unione Matematica Italiana
VL - 8-B
IS - 3
SP - 615
EP - 628
AB - Si studiano soluzioni positive dell’equazione $-\epsilon^{2} \Delta u+u=u^p$ in $\Omega$, dove $\Omega\subseteq \mathbb{R}^{n}$ , $p > 1$ ed $\epsilon$ è un piccolo parametro positivo. Si impongono in genere condizioni al bordo di Neumann. Quando $\epsilon$ tende a zero, dimostriamo esistenza di soluzioni che si concentrano su curve o varietà.
LA - ita
UR - http://eudml.org/doc/195387
ER -

References

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