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Sign-changing solutions for critical Hamiltonian systems in $\mathbb{R}^N$ (2506.13077v1)

Published 16 Jun 2025 in math.AP

Abstract: We build infinitely many geometrically distinct non-radial sign-changing solutions for the Hamiltonian-type elliptic systems $$ -\Delta u =|v|{p-1}v\ \hbox{in}\ \mathbb{R}N,\ -\Delta v =|u|{q-1}u\ \hbox{in}\ \mathbb{R}N,$$ where the exponents $(p,q)$ satisfy $p,q>1$ and belong to the critical hyperbola $$\frac1{p+1}+\frac1{q+1} =\frac {N-2}N.$$ 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.

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