Symmetric solutions for an elliptic partial differential equation that arises in stochastic production planning with production constraints

Abstract

In this article we consider the question of the existence of positive symmetric solutions to the problems of the following type Δu=a(|x|)h(u)+b(|x|)g(u) for x∈RN, which are called entire large solutions. Here N ≥ 3, and we assume that a and b are nonnegative continuous spherically symmetric functions on RN. We extend results previously obtained for special cases of h and g and we will describe a real-world model in which such problems may arise.