Positive supersolutions of non-autonomous quasilinear elliptic equations with mixed reaction (Q6080100)

Given an exterior domain \(\Omega\) in \(\mathbb{R}^N\), the authors present new Liouville-type theorems for positive supersolutions of the elliptic problem \[ -\Delta_p u +b(x) |\nabla u|^{\frac{pq}{q+1}}=c(x)u^q,\text{ in }\Omega, \] where \(N\geq p>1\), \(q\geq p-1\), \(\Delta_p\) denotes the \(p\)-Laplacian and \(b,c\) are some weight functions. A main tool in the their proofs is a generalized Hardy-type inequality associated to the \(p\)-Laplace operator.