PORTUGALIAEMATHEMATICA
Vol. 63, No. 2, pp. 157-171 (2006)
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PORTUGALIAE MATHEMATICA 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. SoaresCMAF 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.
© 2006 Sociedade Portuguesa de Matemática
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