Malchiodi, Andrea:
Costruzione di spike-layers multidimensionali
Bollettino dell'Unione Matematica Italiana Serie 8 8-B (2005), fasc. n.3, p. 615-628, Unione Matematica Italiana (Italian)
pdf (261 Kb), djvu (185 Kb). | MR2182419 | Zbl 1182.35121
Sunto
Si studiano soluzioni positive dellequazione $-\epsilon^{2} \Delta u+u=u^p$ 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.
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Con il contributo del Ministero per i Beni e le Attività Culturali