Let D be a domain in with smooth boundary and consider the problem
The authors study the “largest” solution of (*), which can be defined via two different recipes. Writing S for the set of all solutions to (*), we define U by , and we define V by , where solves in D, on . Under suitable technical assumptions on f (e.g. , f is differentiable and increasing, and the anti-derivative F given by satisfies is integrable at infinity), the authors assert that and they describe the behavior of V and near .