| Abstract: |
| This talk concerns with the existence of positive solutions of a coupled semi-linear elliptic system defined in a cylinder. The system couples an equation defined in the whole cylinder $\Omega$ with another equation defined at the bottom of the cylinder $\Omega'\times\{0\}$. We provide a priori $L^\infty$ bounds for all positive solutions of the system when the nonlinear terms satisfy certain growth conditions. Using the a priori bounds and topological arguments, we prove the existence of positive solutions for these particular semi-linear elliptic systems. |
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