Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 63, No. 2, pp. 157-171 (2006)

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On the concentration of solutions of singularly perturbed Hamiltonian systems in $\mathbb{R}^N$

Miguel Ramos and Sérgio H.M. Soares

CMAF and Faculty of Sciences, Universidade de Lisboa,
Av. Prof. Gama Pinto 2, 1649-003 Lisboa -- PORTUGAL
Departamento de Matemática, ICMC, Universidade de Sao Paulo,
Av. Trabalhador Saocarlense 400, 13560-970 Sao Carlos -- BRAZIL

Abstract: We consider a system of the form $-\varepsilon^2\Delta u+a(x)u=g(v)$, $-\varepsilon^2\Delta v+a(x)v=f(u)$ in $\R^N$, $N\geqslant 3$ and $f$ and $g$ are power-type nonlinearities having superlinear and subcritical growth at infinity. We establish that the least energy solutions to such a system concentrate at global minimum points of $a$ as $\varepsilon\to 0$.

Keywords: superlinear elliptic systems; spike-layered solutions; positive solutions; minimax methods.

Classification (MSC2000): 35J50, 58E05.

Full text of the article:

Electronic version published on: 7 Mar 2008.

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