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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