Abstract
We prove the existence and nonexistence of positive solutions for the system \begin{equation*} \left\{ \begin{array}{c} -\Delta u_{1}=\mu _{1}f_{1}(u_{2})\ \text{ in }\Omega , \\ -\Delta u_{2}=\mu _{2}f_{2}(u_{1}) \ \text{ in }\Omega , \\ \ \ \ \ \ \ \ u_{1}=u_{2}=0 \ \ \ \ \text{ on }\partial \Omega , \end{array} \right. \end{equation*} where $\Omega $ is a bounded domain in $\mathbb{R}^{n\text{ }}$with smooth boundary $ \partial \Omega ,$ $\mu _{i}$ are positive parameters, and $ f_{i}:(0,\infty )\rightarrow \mathbb{R}$ are asymptotically linear at $ \infty $ and allowed to be singular at $0,$ $i=1,2$.
Citation
D.D. Hai. "Singular elliptic systems with asymptotically linear nonlinearities." Differential Integral Equations 26 (7/8) 837 - 844, July/August 2013. https://doi.org/10.57262/die/1369057819
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