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arXiv · 2610.17941

Cubic Nonlinear Schrödinger Systems and Orthonormal Fermionic Ground States in $\mathbb R$

Bin Chen·Yujin Guo·Yong Luo·Juncheng Wei
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Abstract

We study the one-dimensional nonlinear Schrödinger system \[ -u_i''-2\Big(\sum_{k=1}^N u_k^2\Big)^{p-1}u_i=μ_i u_i \quad \mbox{in } \ \mathbb R,\ \ i=1,2,\cdots,N, \tag{S} \] where $u=(u_1,\cdots,u_N)\in H^1(\mathbb{R})^N$, $μ_1\leqμ_2\leq\cdots\leqμ_N<0$, $1 0$ such that $J_N(p)$ is attained for any $p\in(2-δ_N,2)$, whereas $J_N(p)$ is not attained for any $p\in[2,2+δ_N)$. These settle some conjectures of [Gontier--Lewin--Nazar, ARMA, 2021] and [Frank--Gontier--Lewin, CMP, 2021].

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Bin Chen, Yujin Guo, Yong Luo, Juncheng Wei. 2026-10-13. Cubic Nonlinear Schrödinger Systems and Orthonormal Fermionic Ground States in $\mathbb R$. https://arxiv.org/abs/2610.17941

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