scholarly journals Inverse Nodal Problems for the Sturm-Liouville Operator with Some Nonlocal Integral Conditions

2019 ◽  
Vol 07 (01) ◽  
pp. 111-122
Author(s):  
Xiaojuan Qin ◽  
Yunlan Gao ◽  
Congmin Yang
Keyword(s):  
Liouville Operator ◽  
Integral Conditions ◽  
Inverse Nodal Problems ◽  
Sturm Liouville ◽  
Nonlocal Integral Conditions

Inverse nodal problems for the Sturm–Liouville operator with nonlocal integral conditions

2017 ◽  
Vol 25 (6) ◽  
Author(s):  
Yi-Teng Hu ◽  
Chuan-Fu Yang ◽  
Xiao-Chuan Xu
Keyword(s):  
Potential Function ◽  
Liouville Equation ◽  
Liouville Operator ◽  
Dense Subset ◽  
Integral Conditions ◽  
End Points ◽  
Nodal Points ◽  
Inverse Nodal Problems ◽  
Sturm Liouville ◽  
Nonlocal Integral Conditions

AbstractIn this work, we consider inverse nodal problems of the Sturm–Liouville equation with nonlocal integral conditions at two end-points. We prove that a dense subset of nodal points uniquely determine the potential function of the Sturm–Liouville equation up to a constant.

Inverse nodal problems for integro-differential operators with a constant delay

2019 ◽  
Vol 27 (4) ◽  
pp. 501-509 ◽  
Author(s):  
Murat Sat ◽  
Chung Tsun Shieh
Keyword(s):  
Integral Operator ◽  
Potential Function ◽  
Liouville Operator ◽  
Differential Operators ◽  
Constant Delay ◽  
Nodal Points ◽  
Inverse Nodal Problems ◽  
Volterra Integral Operator ◽  
Sturm Liouville

Abstract We study inverse nodal problems for Sturm–Liouville operator perturbed by a Volterra integral operator with a constant delay. We have estimated nodal points and nodal lengths for this operator. Moreover, by using these data, we have shown that the potential function of this operator can be established uniquely.

scholarly journals Reconstruction of the Sturm-Liouville operators on a graph with $\delta'_s$ couplings

2011 ◽  
Vol 42 (3) ◽  
pp. 329-342 ◽  
Author(s):  
ChuanFu Yang
Keyword(s):  
Uniqueness Theorem ◽  
Liouville Operator ◽  
Dense Subset ◽  
Star Graph ◽  
Central Vertex ◽  
Inverse Nodal Problems ◽  
Sturm Liouville ◽  
The Given ◽  
The Uniqueness Theorem ◽  
Liouville Operators

Inverse nodal problems consist in constructing operators from the given zeros of their eigenfunctions. In this work, we deal with the inverse nodal problems of reconstructing the Sturm- Liouville operator on a star graph with $\delta'_s $ couplings at the central vertex. The uniqueness theorem is proved and a constructive procedure for the solution is provided from a dense subset of zeros of the eigenfunctions for the problem as a data.

Sign in / Sign up

Export Citation Format

Share Document