The purpose of this paper is to state some qualitative properties of the solutions to the Emden-Fowler equation $\Delta u + r^\sigma u^p = 0$ in a cone with Dirichlet boundary conditions. Namely one can show that every solution has the same symmetry as the cone in some sense; furthermore it is possible to extend the nonexistence results for regular solutions to this equation already stated by C. Bandle and M. Essen in . For this one needs to establish some asymptotics for the solutions as $r\rightarrow 0$ or $r\rightarrow \infty$, relying on methods used by Veron in  for similar equations, but in different geometries, and then use a special form of the moving-planes method on a sphere in the spirit of .
"Symmetry and nonexistence results for Emden-Fowler equations in cones." Differential Integral Equations 14 (8) 897 - 912, 2001. https://doi.org/10.57262/die/1356123171