# Entire nodal solutions to the critical Lane-Emden system

## TL;DR

This paper proves the existence of multiple nonradial sign-changing solutions to the critical Lane-Emden system in , using limit profiles of symmetric minimizing sequences for a related higher-order problem.

## Contribution

It establishes the existence of finitely many nonradial solutions to the critical Lane-Emden system on , which was previously unknown.

## Key findings

- Existence of finitely many sign-changing solutions.
- Solutions are nonradial and arise as limits of symmetric sequences.
- Results apply to the critical hyperbola rac{1}{p}+rac{1}{q}=rac{N-2}{N}.

## Abstract

We establish the existence of finitely many sign-changing solutions to the Lane-Emden system $$-\Delta u=|v|^{q-2}v,\quad -\Delta v=|u|^{p-2}u \quad \text{ in }\mathbb{R}^N, \ \ N\geq 4,$$ where the exponents $p$ and $q$ lie on the critical hyperbola $\frac{1}{p}+\frac{1}{q}=\frac{N-2}{N}$. These solutions are nonradial and arise as limit profiles of symmetric sign-changing minimizing sequences for a critical higher-order problem in a bounded domain.