Sign-changing solutions for critical Hamiltonian systems in ${\mathbb{R}}^N$

We build infinitely many geometrically distinct non-radial sign-changing solutions for the Hamiltonian-type elliptic systems $$-\mathrm{\Delta }u=\mathrm{\mid }v{\mathrm{\mid }}^{p-1}v\text{in}{\mathbb{R}}^N,-\mathrm{\Delta }v=\mathrm{\mid }u{\mathrm{\mid }}^{q-1}u\text{in}{\mathbb{R}}^N,$$ where the exponents $(p,q)$ satisfy $p,q>1$ and belong to the critical hyperbola $$\frac{1}{p+1}+\frac{1}{q+1}=\frac{N-2}{N}\mathrm{.}$$ To establish this result, we introduce several new ideas and strategies that are both robust and potentially applicable to other critical problems lacking the Kelvin invariance.