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Construction of multidimensional spike-layers

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  • 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.
    Mathematics Subject Classification: Primary: 35J25, 35J20; Secondary: 35B38.

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