Costruzione di spike-layers multidimensionali

Malchiodi, Andrea

Bollettino dell'Unione Matematica Italiana, Tome 8-A (2005), p. 615-628 / Harvested from Biblioteca Digitale Italiana di Matematica

Résumé

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.

Abstract

We study positive solutions of the equation $-\epsilon^{2} \Delta u+u=u^p$ in $\Omega$, where $\Omega\subseteq \mathbb{R}^{n}$ , $p>1$ and $\epsilon$ is a positive small parameter. Usually we put Neumann boundary conditions. When $\epsilon$ goes to zero, we prove the existence of solutions which concentrate on curves or varietis.

Détail

Publié le : 2005-10-01

MR 2182419 | Zbl 1182.35121

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