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

TL;DR

This paper investigates the existence of positive symmetric solutions to a class of elliptic partial differential equations with applications in stochastic production planning, extending previous results to more general functions.

Contribution

It generalizes prior findings by establishing conditions for symmetric solutions to a broader class of elliptic PDEs with applications in real-world production models.

Findings

Established existence of symmetric solutions for generalized PDEs

Extended previous results to more general functions h and g

Connected mathematical results to practical production planning models

Abstract

In this article we consider the question of the existence of positive symmetric solutions to the problems of the following type $\Delta u=a\left( \left\vert x\right\vert \right) h\left( u\right) +b\left( \left\vert x\right\vert \right) g\left( u\right) $ for $x\in \mathbb{R}^{N}$, which are called entire large solutions. Here $N\geq 3$, and we assume that $a$ and $b$ are nonnegative continuous spherically symmetric functions on $\mathbb{R}% ^{N} $. 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.