We consider positive solutions of the equation $- $ε$^2 $Δ $u + u $=$u^p$ in $\Omega$, where $\Omega \subseteq \R^n$, $p > 1$ and ε is a small positive parameter. Neumann boundary conditions are imposed in general. We prove existence of solutions which concentrate at curves or manifolds in $\overline{\Omega}$ when ε → 0.
Construction of multidimensional spike-layers
Malchiodi, Andrea
2006
Abstract
We consider positive solutions of the equation $- $ε$^2 $Δ $u + u $=$u^p$ in $\Omega$, where $\Omega \subseteq \R^n$, $p > 1$ and ε is a small positive parameter. Neumann boundary conditions are imposed in general. We prove existence of solutions which concentrate at curves or manifolds in $\overline{\Omega}$ when ε → 0.File in questo prodotto:
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