Author

Wei Ji

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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

Finitely many solutions for the prescribed scalar curvature problem at the critical flatness order

We study the following prescribed scalar curvature problem $$ -\Delta u=K(y)u^{2^*-1},\ \ u>0 \,\ \ \text{in}\ \ \mathbb{R}^N, $$ where $2^*=\frac{2N}{N-2}$. For $N\geq4$, we construct a positive $K(y)$ with maximum set $\{|y|=1\}$ and critical order of flatness $m=N-2$ at $|y|=1$, such that the equation admits only fi...

Wei Ji, Yi-Xing Pu · 0 citations