An elliptic partial differential equation and its application

This paper deals with the following elliptic equation -2 sigma(2)Delta z + vertical bar del z vertical bar(2) + 4 alpha z = 4 vertical bar x vertical bar(2) for x is an element of R-N, (N >= 1), where alpha > 0, and sigma > 0 are some real constants. The solution method is based on the sub- and super-solutions approach. The case N > 1 seemed not considered before. This equation models a stochastic production planning problem. (C) 2019 Elsevier Ltd. All rights reserved.