Sign-changing solutions for critical Hamiltonian systems in $\mathbb{R}^N$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916795241201664 |
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| author | Guo, Yuxia Kim, Seunghyeok Pistoia, Angela Yan, Shusen |
| author_facet | Guo, Yuxia Kim, Seunghyeok Pistoia, Angela Yan, Shusen |
| contents | We build infinitely many geometrically distinct non-radial sign-changing solutions for the Hamiltonian-type elliptic systems $$ -Δu =|v|^{p-1}v\ \hbox{in}\ \mathbb{R}^N,\ -Δv =|u|^{q-1}u\ \hbox{in}\ \mathbb{R}^N,$$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13077 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sign-changing solutions for critical Hamiltonian systems in $\mathbb{R}^N$ Guo, Yuxia Kim, Seunghyeok Pistoia, Angela Yan, Shusen Analysis of PDEs We build infinitely many geometrically distinct non-radial sign-changing solutions for the Hamiltonian-type elliptic systems $$ -Δu =|v|^{p-1}v\ \hbox{in}\ \mathbb{R}^N,\ -Δv =|u|^{q-1}u\ \hbox{in}\ \mathbb{R}^N,$$ 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. |
| title | Sign-changing solutions for critical Hamiltonian systems in $\mathbb{R}^N$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2506.13077 |