Quasilinear Riccati-Type Equations with Oscillatory and Singular Data

We characterize the existence of solutions to the quasilinear Riccati-type equation with a distributional or measure datum σ. Here is a quasilinear elliptic operator modeled after the -Laplacian ( ), and Ω is a bounded domain whose boundary is sufficiently flat (in the sense of Reifenberg). For distributional data, we assume that and . For measure data, we assume that they are compactly supported in Ω, , and is in the sub-linear range . We also assume more regularity conditions on and on in this case.