The Principal Eigenvalue for a Class of Singular Quasilinear Elliptic Operators and Applications

We characterize the principal eigenvalue associated to the singular quasilinear elliptic operator \(-\Delta u - \mu (x) \frac{|\nabla u|^q}{u^{q-1}}\) in a bounded smooth domain \(\Omega \subset \mathrm{I\!R}^N\) with zero Dirichlet boundary conditions. Here, \(1\frac{N}{2}\).