TITLE

# Solutions with multiple spike patterns for an elliptic system

AUTHOR(S)
Ramos, Miguel; Tavares, Hugo
PUB. DATE
January 2008
SOURCE
Calculus of Variations & Partial Differential Equations;Jan2008, Vol. 31 Issue 1, p1
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
We consider a system of the form $$- \varepsilon^2 \Delta u + V(x)u=g(v)$$ , $$-\varepsilon^2 \Delta v + V(x)v=f(u)$$ in an open domain $$\Omega$$ of $${\mathbb{R}}^N$$ , with Dirichlet conditions at the boundary (if any). We suppose that f and g are power-type non-linearities, having superlinear and subcritical growth at infinity. We prove the existence of positive solutions $$u_{\varepsilon}$$ and $$v_{\varepsilon}$$ which concentrate, as $$\varepsilon\to 0$$ , at a prescribed finite number of local minimum points of V( x), possibly degenerate.
ACCESSION #
26762578

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