Abstract.
We consider a system of the form \(-\varepsilon^{2}\triangle u+u = g(\upsilon), -\varepsilon^{2}\triangle \upsilon+\upsilon = f(u)\) in Ω with Dirichlet boundary condition on \(\partial\Omega\), where Ω is a smooth bounded domain in \({\mathbb{R}}^{N}, N\geq3\) and f, g are power-type nonlinearities having superlinear and subcritical growth at infinity. We prove that the least energy solutions to such a system concentrate, as \(\varepsilon\) goes to zero, at a point of Ω which maximizes the distance to the boundary of Ω.
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Received and accepted 15 January 2005
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Pistoia, A., Ramos, M. Locating the peaks of the least energy solutions to an elliptic system with Dirichlet boundary conditions. Nonlinear differ. equ. appl. 15, 1–23 (2008). https://doi.org/10.1007/s00030-007-4066-8
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DOI: https://doi.org/10.1007/s00030-007-4066-8