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

Abstract

We build infinitely many geometrically distinct non-radial sign-changing solutions for the Hamiltonian-type elliptic systems $$-\hat{I}”u=|v{|}^{p-1}vin{\mathbb{R}}^N,-\hat{I}”v=|u{|}^{q-1}uin{\mathbb{R}}^N,$$ where the exponents $(p,q)$ satisfy $p,q>1$ and belong to the critical hyperbola $$\frac{1}{p+1}+\frac{1}{q+1}=\frac{N-2}{N}.$$ 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.

53 pages