Sharp estimates, uniqueness and nondegeneracy of positive solutions of the Lane-Emden system in planar domains

Zhijie Chen, Houwang Li, Wenming Zou

We study the Lane-Emden system $$\{\begin{array}{l}-\Delta u=v^p,u>0,\text{in}\Omega ,-\Delta v=u^q,v>0,\text{in}\Omega ,u=v=0,\text{on}\partial \Omega ,\end{array}$$ where $Ω\subset…