Chuan-Fu Yang’s research while affiliated with Nanjing University of Science and Technology and other places

... Very recently, progress has been made in the nonlinear case in the paper [10], by proving that two spectra uniquely determine potentials if a ∈ [2π/5, π/2), yet it is not possible in the case when a ∈ [π/3, 2π/5). In [26], more research has been conducted for the case where a ∈ [2π/5, π/2) by giving a necessary and sufficient condition for the solvability and formulating the stability of the inverse problem. The question of whether two spectra are enough to uniquely recover potentials for a < π/3 remained unanswered. ...

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Inverse problem for Dirac operators with a small delay

... In a different context, rotation vectors and rotation sets appear in the interesting works [2,12,[15][16][17] (see also the references therein). Various cases of rotations are of great interest in many theoretical problems and applications (see, e.g., [7,8,18,20,22] ). ...

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Poincaré Type Results on a k-Dimensional Torus

... There is also considerable number of results related to the Sturm-Liouville operators with two constant delays (see [4,14,[19][20][21][22][23]). In recent years, a significant number of results related to the inverse problems for Sturm-Liouville operators, have been extended to Dirac operators with one delay (see [3,10,25,26]), as well as to Dirac operators with two delays (see [24]). ...

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On Recovering Dirac Operators with Two Delays

... Finally, it is worth noting that Ambarzumyan-type theorems for the problems B ν (q)(ν = 0, 1) are obtained in [21] and that the inverse nodal problem for the problem B 1 (q) is studied in [28]. In fact, Ambarzumyan-type theorems for the Sturm-Liouville operators on trees of general structure have been obtained by Carlson and Pivovarchik [5]. ...

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Traces for Sturm–Liouville Operators on a Caterpillar Graph

... An extension of the above control problem to graphs requires an appropriate definition of the functional-differential equation with delay on them. However, various functional-differential and other classes of nonlocal operators on graphs until recently were considered only in the locally nonlocal case, when the corresponding nonlocal equation on each edge can be solved independently of the equations on the other edges [26][27][28][29][30][31][32]. This limitation always left unclear how the nonlocalities could coexist with the internal vertices of the graph and, in particular, how one could describe a process with global aftereffect on the entire graph. ...

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On damping a control system with global aftereffect on quantum graphs: Stochastic interpretation

... While there are a number of results about both direct and inverse problems for various difference or differential operators, see [14][15][16][17][18][19][20][21][22], there are just a few results related to differential operators with two or more delays, see [23,24]. Inspired by the above mentioned literatures, the purpose of this paper is to study the nonlinear inverse problem for Sturm-Liouville operator with multiple delays. ...

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Uniqueness of Nonlinear Inverse Problem for Sturm–Liouville Operator with Multiple Delays

... There are sufficient prerequisites for the existence and uniqueness of the inverse problem solution. Many authors [22][23][24][25][26][27][28][29] have discussed the existence and uniqueness of the solution of an inverse problem for a differential equation. Fadi Awawdeh [22] have solved the second-order inverse problem using perturbation method. ...

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An investigation of an inverse problem for second-order abstract differential equation

... A quantum graph is a metric graph that carries differential operators on the edges with appropriate conditions on the vertices. Inverse spectral problems on quantum graphs usually aim at determining graph structures or differential operators from spectral data, see e.g, [4,6,11,19,27,36,39,46,47,49]. Many other inverse problems that are closely related to inverse spectral problems have also found the counterparts on graphs. ...

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Vertex weight reconstruction in the Gel'fand's inverse problem on connected weighted graphs

... In recent years, such problem has aroused the research interest of many scholars since the important applications of the Dirac system. There are extensive literatures on the Dirac operator with interface conditions and eigenparameter-dependent boundary conditions; the research focuses on the properties of eigenvalues and eigenfunction, inverse problems, sampling theories, and so on; for more details, see [26,[30][31][32][33][34][35][36][37][38] and references cited therein. ...

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Spectral properties for discontinuous Dirac system with eigenparameter‐dependent boundary condition

... In 2020, Bondarenko [14] studied the local solvability and stability for the non-self-adjoint inverse Sturm-Liouville problems with the both Robin or both Dirichlet boundary conditions by using the method of spectral mappings. The results of Borg have also been generalized into many other problems, such as the transmission eigenvalue problems [15,16], the discontinuous problems [17,18], the problems with non-separated boundary conditions [19,20], and other problems [6,[21][22][23]. Without the local solvability, there are also many works only related to the stability (see, e.g., [12,[24][25][26][27][28][29][30][31][32][33][34] and other works). ...

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Weak and strong stability of the inverse Sturm‐Liouville problem