Uniqueness of a positive solution to the Dirichlet problem for a quasilinear equation with \(p\)-Laplacian in a ball
The author proves the existence of a unique, positive, radial solution for the equation \(\Delta_p u + |x|^m |u|^q = 0 \) in the unit ball in \(\mathbb{R}^n\) with \(n\geq 2\) with zero Dirichlet boundary conditions. For \(1<p \leq 2\) (in the case \(n = 2\), \(1< p<2\)), if \(1 < q \leq \frac{(p-1)(m+n)}{n-p}\), it is shown that the problem admits a unique, positive, radial solution.
quasilinear equation with \(p\)-Laplacian
scientific article; zbMATH DE number 5975562