Concentration phenomena in weakly coupled elliptic systems with critical growth* |
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| Authors: | Email author" target="_blank">Riccardo?MolleEmail author Angela?Pistoia |
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| Institution: | 1.Dipartimento di Matematica,Università di Roma “Tor Vergata”,Roma,ITALIA;2.Dipartimento di Metodi e Modelli Matematici,Università di Roma “La Sapienza”,Roma,ITALIA |
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| Abstract: | In this paper we consider the weakly coupled elliptic system with critical growth where a, b, c, d are C
1-functions defined in a bounded regular domain  of 
N
. Here we construct families of solutions which blow-up and concentrate at some points in as the positive parameter  goes to zero.*The authors are supported by M.I.U.R., project  Metodi variazionali e topologici nello studio di fenomeni non lineari . |
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| Keywords: | :" target="_blank">: elliptic systems critical nonlinearity Dirichlet boundary condition |
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\left\{ {\begin{array}{*{20}l}
{{ - \Delta u = {\left| u \right|}^{{\frac{4}
{{N - 2}}}} u + \varepsilon {\left {a{\left( x \right)}u + b{\left( x \right)}v} \right]}} \hfill} & {{{\text{in}}\Omega ,} \hfill} \\
{{ - \Delta v = {\left| v \right|}^{{\frac{4}
{{N - 2}}}} v + \varepsilon {\left {c{\left( x \right)}u + d{\left( x \right)}v} \right]}} \hfill} & {{{\text{in}}\Omega ,} \hfill} \\
{{u = v = 0} \hfill} & {{{\text{on}}\partial \Omega ,} \hfill} \\
\end{array} } \right.
$$](/content/n8nh5ejwvckn0mql/574_2004_Article_22_TeX2GIFEqu1.gif)