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Existence and multiplicity of positive solutions for elliptic systems. (English) Zbl 0885.35028
The authors investigate the existence and multiplicity of positive radial solutions for boundary value problems of the form $$\Delta u+\lambda k_1(|x|)f(u,v)= 0,\quad \Delta v+\mu k_2(|x|)g(u,v)=0$$ in a domain $\Omega= \{x\in\bbfR^N: 0< R_1<|x|< R_2\}$, $u|_{\partial\Omega}= v|_{\partial\Omega}= 0$. The results are formulated in terms of $f_0= \lim_{(u,v)\to 0} f(u,v)/(u+ v)$, $g_0= \lim_{(u,v)\to 0} g(u,v)/(u+ v)$, $f_\infty=\lim_{(u,v)\to\infty} f(u,v)/(u+ v)$, $g_\infty= \lim_{(u,v)\to\infty} g(u,v)/(u+v)$.

MSC:
35J55Systems of elliptic equations, boundary value problems (MSC2000)
35J65Nonlinear boundary value problems for linear elliptic equations
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References:
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