# On the solutions of the critical Lane-Emden equation in higher space dimensions

## TL;DR

This paper investigates solutions to the critical Lane-Emden equation in higher dimensions, demonstrating that solutions can be expressed via elliptic functions after specific transformations, focusing on real solutions relevant for physical applications.

## Contribution

It introduces a method to represent solutions of the critical Lane-Emden equation in higher dimensions using elliptic functions, expanding understanding of their structure.

## Key findings

- Solutions can be expressed in terms of elliptic functions
- Transformations simplify the equation to a solvable form
- Focus on real solutions for physical relevance

## Abstract

In this paper we study solutions of the critical Lane-Emden equation in higher space dimensions. We show that after certain transformations the general solution can be written in terms of elliptic functions. We restrict ourselves to real solutions which can be used in physical applications.