X. Zhong

activity

20222026

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math.AP2026

Spectral-Edge Continuation, Dimensional Crossover, and Endpoint Stability for Partially Confined Nonlinear Schrödinger Equations

Xuexiu Zhong

We study the global geometry and endpoint dynamics of positive solutions of $- Δ u + ∣ y ∣^{2} u + λ u = g (u)$ , $(y, z) \in R^{d} \times R^{m}$ , $m = N - d$ . Despite the loss of coercivity at…

math.AP2026

Liouville theorems and symmetry of positive solutions for partially confined nonlinear Schrödinger equations

Zhijie Chen, Youjun Wang, Jianjun Zhang +1

We study positive solutions of the partially confined stationary nonlinear Schrödinger equation $$-Δu+|y|^2u+λu=g(u),\quad (y,z)\in\mathbb{R}^d\times\mathbb{R}^{m},\quad 1\leq d<N,…