Positive solutions to singular non-linear Schrödinger-type equations

Abstract

We study the existence and nonexistence of positive (super) solutions to a singular quasilinear second-order elliptic equations with structural coefficients from non-linear Kato-type classes. Under certain general assumptions on the behaviour of the coefficient at infinity we construct an entire positive solution in R^N which is bounded above and below by positive constants. An application is given to a non-existence problem in an exterior domain.