共查询到20条相似文献,搜索用时 927 毫秒
1.
V. Yurko 《Applicable analysis》2013,92(1-2):63-77
The inverse spectral problem of recovering pencils of second-order differential operators on the half-line is studied. We give a formulation of the inverse problem, prove the uniqueness theorem and provided a procedure for constructing the solution of the inverse problem. We also establishe connections with inverse problems for partial differential equations. 相似文献
2.
V. Yurko 《Journal of Mathematical Analysis and Applications》2006,320(1):439-463
The inverse spectral problem of recovering pencils of second-order differential operators on the half-line with turning points is studied. We establish properties of the spectral characteristics, give a formulation of the inverse problem, prove a uniqueness theorem and provide a constructive procedure for the solution of the inverse problem. 相似文献
3.
V. Yurko 《Journal of Differential Equations》2008,244(2):431-443
We study boundary value problems on compact graphs without circles (i.e. on trees) for second-order ordinary differential equations with nonlinear dependence on the spectral parameter. We establish properties of the spectral characteristics and investigate the inverse spectral problem of recovering the coefficients of the differential equation from the so-called Weyl vector which is a generalization of the Weyl function (m-function) for the classical Sturm-Liouville operator. For this inverse problem we prove the uniqueness theorem and obtain a procedure for constructing the solution by the method of spectral mappings. 相似文献
4.
V. A. Yurko 《Differential Equations》2008,44(12):1721-1729
We study boundary value problems on noncompact cycle-free graphs (i.e., trees) for second-order ordinary differential equations with a nonlinear dependence on the spectral parameter. We establish properties of the spectrum and analyze the inverse problem of reconstructing the coefficients of a differential equation on the basis of the so-called Weyl functions. For this inverse problem, we prove a uniqueness theorem and obtain a procedure for constructing the solution by the method of spectral mapping. 相似文献
5.
Vjacheslav Yurko 《Complex Analysis and Operator Theory》2016,10(6):1203-1212
Non-self-adjoint second-order differential pencils on a finite interval with non-separated quasi-periodic boundary conditions and jump conditions are studied. We establish properties of spectral characteristics and investigate the inverse spectral problem of recovering the operator from its spectral data. For this inverse problem we prove the corresponding uniqueness theorem and provide an algorithm for constructing its solution. 相似文献
6.
Vyacheslav Yurko 《Central European Journal of Mathematics》2014,12(3):483-499
We study inverse spectral problems for ordinary differential equations on compact star-type graphs when differential equations have different orders on different edges. As the main spectral characteristics we introduce and study the so-called Weyl-type matrices which are generalizations of the Weyl function (m-function) for the classical Sturm-Liouville operator. We provide a procedure for constructing the solution of the inverse problem and prove its uniqueness. 相似文献
7.
V. A. Yurko 《Differential Equations》2011,47(1):50-59
We study the inverse problem of spectral analysis for Sturm-Liouville operators on A-graphs. We obtain a constructive procedure
for solving the inverse problem of reconstruction of coefficients of differential operators from spectra and prove the uniqueness
of the solution. 相似文献
8.
V. Yurko 《Results in Mathematics》2005,48(3-4):371-386
Inverse spectral problems are studied for non-selfadjoint systems of ordinary differential equations on a finite interval. We establish properties of the spectral characteristics, and provide a procedure for constructing the solution of the inverse problem of recovering the coefficients of differential systems from the given spectral characteristics. 相似文献
9.
V. A. Yurko 《Journal of Mathematical Sciences》2008,150(6):2620-2627
The inverse spectral problem of recovering pencils of second-order differential operators on the half-line with turning points
is studied. We give a formulation of the inverse problem, establish properties of the spectral characteristics, and prove
the uniqueness theorem for the solution of the inverse problem.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 5, pp. 237–246, 2006. 相似文献
10.
V. A. Yurko 《Mathematical Notes》2011,89(3-4):438-449
We study the inverse spectral problem for Sturm-Liouville differential operators on hedgehog-type graphs with a cycle and with standard matching conditions at interior vertices. We prove a uniqueness theorem and obtain a constructive solution for this class of inverse problems. 相似文献
11.
We study non-self-adjoint second-order differential operators with a constant delay. We establish properties of the spectral characteristics and investigate the inverse problem of recovering operators from their spectra. The uniqueness theorem is proved for this inverse problem. 相似文献
12.
Direct and inverse problems of spectral analysis are studied for an indefinite singular boundary value problem coming from astrophysics. We establish properties of the spectrum, prove completeness and expansion theorems and investigate the inverse problem of recovering the differential equation from the given spectral characteristics. 相似文献
13.
We consider second-order functional differential operators with a constant delay. Properties of their spectral characteristics are obtained and a nonlinear inverse problem is studied, which consists in recovering the operators from their spectra. We establish the uniqueness and develop a constructive algorithm for solution of the inverse problem. 相似文献
14.
We study Sturm–Liouville differential operators on noncompact graphs without cycles (i.e., on trees) with standard matching
conditions in internal vertices. First we establish properties of the spectral characteristics and then we investigate the
inverse problem of recovering the operator from the so-called Weyl vector. For this inverse problem we prove a uniqueness
theorem and propose a procedure for constructing the solution using the method of spectral mappings.
Received: February 13, 2007. 相似文献
15.
The inverse problem of synthesizing parameters of differential systems having a finite number of arbitrary order singularities and turning points is investigated. We establish properties of the spectral characteristics, prove a uniqueness theorem and provide a prodcedure for constructing the solution of the inverse problem. 相似文献
16.
We investigate a problem for the Dirac differential operators in the case where an eigenparameter not only appears in the
differential equation but is also linearly contained in a boundary condition. We prove uniqueness theorems for the inverse
spectral problem with known collection of eigenvalues and normalizing constants or two spectra. 相似文献
17.
We investigate boundary-value problems for differential equations with singularity and discontinuity conditions inside an interval. We describe properties of the spectrum, prove a theorem on the completeness of eigenfunctions and associated functions, and study the inverse spectral problem. 相似文献
18.
V. A. Yurko 《Proceedings of the Steklov Institute of Mathematics》2006,255(1):260-274
Inverse spectral problems are studied for non-self-adjoint systems of ordinary differential equations on a finite interval.
We establish properties of spectral characteristics and provide a procedure for constructing the solution of the inverse problem
of recovering the coefficients of differential systems from given spectra.
Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2006, Vol. 255, pp. 273–287. 相似文献
19.
We consider an inverse boundary problem for a general second order self-adjoint elliptic differential operator on a compact differential manifold with boundary. The inverse problem is that of the reconstruction of the manifold and operator via all but finite number of eigenvalues and traces on the boundary of the corresponding eigenfunctions of the operator. We prove that the data determine the manifold and the operator to within the group of the generalized gauge transformations. The proof is based upon a procedure of the reconstruction of a canonical object in the orbit of the group. This object, the canonical Schrödinger operator, is uniquely determined via its incomplete boundary spectral data. 相似文献
20.
A mixed problem for the nonlinear Bogoyavlenskii system on the half-line is studied by the inverse problem method. The solution of the mixed problem is reduced to the solution of the inverse spectral problem of recovering a forth-order differential operator on the half-line from the Weyl matrix. We derive evolution equations for the elements of the Weyl matrix and give an algorithm for the solution of the mixed problem. Evolution equations of the elements of the Weyl matrix are nonlinear. It is shown that they can be reduced to a nested system of three successively solvable matrix Riccati equations. 相似文献