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An existence result on positive solutions for a class of semilinear elliptic systems. (English) Zbl 1067.35026

Consider the boundary value problem \(-\Delta v= \lambda f(u)\) in \(\Omega\), \(-\Delta u= \lambda f(v)\) in \(\Omega\), \(u= v\) on \(\partial\Omega\), where \(\lambda\) is a positive parameter and \(\Omega\) is a bounded domain in \(\mathbb R^N\). The authors prove the existence of a large positive solution for large \(\lambda\) when \(\lim_{x\to\infty} (f(Mg(x))/x)= 0\) for every \(M> 0\).

MSC:

35J55 Systems of elliptic equations, boundary value problems (MSC2000)
35J60 Nonlinear elliptic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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