BMO solutions to quasilinear equations of \(p\)-Laplace type (Q2675343)

The main goal of this article is to derive necessary and sufficient conditions for the existence of a BMO solution \(u\geq 0\) to the quasilinear equation \[ -\Delta_p u= \mu\text{ in }\mathbb{R}^N, \] where \(\mu\) is a locally finite Radon measure, and \(\Delta_p u=\operatorname{div}(|\nabla u|^{p-2}\nabla u)\) is the \(p\)-Laplace operator with \(p>1\). Further results included in this work contain a discussion on the related equation \[ -\Delta_p u= \sigma u^q+\mu\text{ in }\mathbb{R}^N, \] where \(q>0\) and \(\sigma\), \(\mu\) are locally finite Radon measures.