Removable isolated singularities of solutions to the weighted \(p\)-Laplacian with singular convection (Q2905706)

The paper deals with nonlinear elliptic equations NEWLINE\[NEWLINE -\text{div} (|x|^\alpha |\nabla u|^{p-2}\nabla u) +\lambda \frac{1}{|x|^\beta}|\nabla u|^{p-2}\nabla u \cdot x = |x|^\gamma g(|x|), NEWLINE\]NEWLINE in \(B\setminus \{0\}\) where \(B\) is the unit ball in \(\mathbb{R}^N\). The boundary conditions are NEWLINE\[NEWLINE|x|^\alpha |\nabla u|^{p-2}\nabla u\cdot \nu = A-\rho u.NEWLINE\]NEWLINE A notion of generalized solution is given and conditions are established so that such generalized solutions exist and have removable singularities.