Author

Yong Luo

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Preprint Oct 2026

Uniqueness of Bound States for Double-Power Scalar Field Equations

We study the uniqueness of bound states for the following scalar field equation $$ -\Delta u+u=-\varepsilon |u|^{q-1}u+|u|^{p-1}u \,\ \ \mbox{in}\,\ \mathbb R^N, \,\ \varepsilon>0,\tag*{$(*)$} $$ where $ N\ge3,\ 11$ satisfies $q \neq p$. For each integer $k \geq 1$, we prove that the equation $(*)$ has, up to translati...

Yu-Jin Guo, Wei Ji, Yong Luo · 1 citation · ⚡1

Preprint Oct 2026

Cubic Nonlinear Schr\"{o}dinger Systems and Orthonormal Fermionic Ground States in $\mathbb R$

We study the one-dimensional nonlinear Schr\"{o}dinger system \[ -u_i''-2\Big(\sum_{k=1}^N u_k^2\Big)^{p-1}u_i=\mu_i u_i \quad \mbox{in } \ \mathbb R,\ \ i=1,2,\cdots,N, \tag{S} \] where $u=(u_1,\cdots,u_N)\in H^1(\mathbb{R})^N$, $\mu_1\leq\mu_2\leq\cdots\leq\mu_N<0$, $1<p<3$ and $N\geq 2$ are arbitrary. For the cubic...

Bin Chen, Yu-Jin Guo, Yong Luo et al. · 0 citations