On positive solutions to nonlinear elliptic equations in cone-like domains (Q1358612)

Let \(x\) be a point in \(\mathbb{R}^n\), \(n\geq 2\), \(K\) be a cone \(\{x:0<r=|x|<\infty, \theta\in\Omega\}\), where \((r,\theta)= (r,\theta_1,\dots,\theta_{n-1})\) are the polar coordinates in \(\mathbb{R}^n\), and \(\Omega\) be a domain on the unit sphere \(S^{n-1}\) whose boundary \(\partial\Omega\) belongs to the \(C^2\) class. We consider the equation \(\Delta u+ r^\sigma u^p=0\) in \(K\), where \(\sigma\in\mathbb{R}\), \(p>1\). We prove some result on nonexistence of positive solutions to this equation.