# American Institute of Mathematical Sciences

January  2006, 14(1): 187-202. doi: 10.3934/dcds.2006.14.187

## Construction of multidimensional spike-layers

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Received  November 2004 Revised  July 2005 Published  October 2005

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.
Citation: Andrea Malchiodi. Construction of multidimensional spike-layers. Discrete and Continuous Dynamical Systems, 2006, 14 (1) : 187-202. doi: 10.3934/dcds.2006.14.187
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