9 papers
Finite-data inverse nodal optimization in angular-momentum sectors of Schrödinger operators
Xijun Deng, Zhisu Liu, Yonghui Xia
In this paper, we study a finite-data inverse nodal optimization problem for radial Schrödinger operators in an arbitrary fixed angular-momentum sector. The analysis is built direc…
Finite inverse nodal problems for singular weighted Sturm--Liouville equations: variational selection and spectral matching
Zhibo Cheng, Yuchao He, Sunan Wang +1
The recent work \cite{HeWuXiaZhang2025} introduced a finite-data inverse nodal framework for regular one-dimensional Sturm-Liouville operators. Nevertheless, formulating a multidim…
A dynamical system framework yielding quantitative inverse spectral results for Sturm-Liouville operators
Yuchao He, Yonghui Xia, Meirong Zhang
This paper establishes a dynamical-system framework that yields quantitative results for the inverse optimal spectral problem of reconstructing a potential from finite ob…
A novel and application-oriented inverse nodal problem for Sturm-Liouville operators
Yuchao He, Mengda Wu, Yonghui Xia +1
This paper develops a methodological framework for addressing a novel and application-oriented inverse nodal problem in Sturm-Liouville operators, having significant applications i…
Variational formulation for stratified steady water wave in two-layer flows
Yuchao He, Yonghui Xia, Zhe Zhou
In this paper, the variational formulation for steady periodic stratified water waves in two-layer flows is given. The critical points of a natural energy functional is proved to b…
Constant vorticity two-layer water flows in the -plane approximation with centripetal forces
Yuchao He, Yongli Song, Yonghui Xia
The constant vorticity {\bf two-layer water wave} in the -plane approximation with centripetal forces is investigated in this paper. Different from the works (Chu and Yang\cite[…
Bifurcation from a blood flow with variable body force
Yuchao He, Yongli Song, Yonghui Xia
This paper investigates the existence of periodic solutions in blood flow propagating through vessels with free boundary conditions via the bifurcation theory. It is rigorously pro…
The eigenvector-eigenvalue identity for the quaternion matrix with its algorithm and computer program
Yuchao He, Mengda Wu, Yonghui Xia
Peter Denton, Stephen Parke, Terence Tao and Xining Zhang [arxiv 2019] presented a basic and important identity in linear commutative algebra, so-called {\bf the eigenvector-eigenv…
Floquet multipliers and the stability of periodic linear differential equations: a unified algorithm and its computer realization
Mengda Wu, Yonghui Xia, Ziyi Xu
Floquet multipliers (characteristic multipliers) play significant role in the stability of the periodic equations. Based on the iterative method, we provide a unified algorithm to…