Entire nodal solutions to the critical Lane-Emden system

Abstract

We establish the existence of finitely many sign-changing solutions to the Lane-Emden system $$-\Delta u=|v{|}^{q-2}v,-\Delta v=|u{|}^{p-2}u\text{ in }{\mathbb{R}}^N,N\ge 4,$$ 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.

21 pages and 1 figure, revised version