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math.AP2023
Observability and unique continuation inequalities for the Schrödinger equations with inverse-square potentials
Hui Xu, Longben Wei, Zhiwen Duan
This paper is inspired by Wang, Wang and Zhang's work [ Observability and unique continuation inequalities for the Schrödinger equation. J. Eur. Math. Soc. 21, 3513--3572 (2019)],…
math.AP2023
Uncertainty Principle and Geometric Condition for the Observability of Schrödinger Equations
Longben Wei, Zhiwen Duan, Hui Xu
We provide necessary and sufficient geometric conditions for the exact observability of the Schrödinger equation with inverse-square potentials on the half-line. These conditions a…
math.AP2018★ 1 cited
Radial symmetry of positive entire solutions of a fourth order elliptic equation with a singular nonlinearity
Zongming Guo, Long Wei, Feng Zhou
The necessary and sufficient conditions for a regular positive entire solution of the biharmonic equation: \begin{equation} \label{0.1} -Δ^2 u=u^{-p} \;\; \mbox{in $\R^N \; (N…