provide a procedure for constructing the
solution of the inverse problem and prove its uniqueness.
Keywords: Geometrical graphs, dierential operators, regular singularities, inverse spectral problems
MSC 2010: 34A55, 34L05, 47E05
Received December 8, 2014; revised February 11, 2015; accepted February 20, 2015
We study inverse spectral problems for variable order dierential equations with regular singularities on
compact star-type graphs. More precisely, dierential equations have dierent orders on dierent edges.
method of spectral mappings.
2010 Mathematics Subject Classification. 34A55, 47E05.
In this paper, we consider the pencil L D L.`; U/ given by the differential
`.Y / WD Y
2I C 2iQ1.x/CQ0.x/
Y; x > 0; (1)
with the initial condition
U.Y / WD Y
0.0/C .ih1 C h0/Y.0/ D 0: (2)
Here Y.x/ D Œyk.x/kD1;:::;m is a column vector, is the spectral parameter, I is
themm unit matrix,Qs.x/ D ŒQs;jk.x/j;kD1;:::;m aremmmatrix-functions,
hs D Œhs;jkj;kD1;:::;m, where hs;jk are complex numbers.
We assume that det.I ˙ h1/ ¤ 0. This
uniqueness theorem and provide a procedure for constructing
Keywords. Geometrical graphs with a cycle, differential pencils, inverse spectral
2010 Mathematics Subject Classification. Primary 34A55; secondary 34B45, 34B07,
Analysis on graphs and other similar structures has been developed for quite some
time due to various applications in applied sciences. In particular in recent years
it has experienced a significant boost in terms of new applications arising and new
methods were developed and studied.
In this paper we study
spectral mappings. A constructive algorithm for the solution of
the inverse problem is provided.
Keywords:Matrix quadratic dierential pencils, spectral data, inverse spectral problems, method of spectral
MSC 2010: 34A55, 34B07, 34B24, 34L40, 47E05
Natalia Bondarenko: Department of Mechanics and Mathematics, Saratov State University, Astrakhanskaya 83,
Saratov 410012, Russia, e-mail: firstname.lastname@example.org
In this paper, we consider the boundary value problem L = L(ℓ, U, V) for the equation
ℓY := Y + (ñ2I + 2iñQ1(x) + Q0(x))Y = 0, x ∈ (0, ð
, heat and moisture transfer, particle swarm optimization,
thickness-heat conductivity-porosity determination, weighted least-squares solution
MSC 2010: 34A55, 65L08, 80A23
Received December 14, 2013; revised June 8, 2014; accepted April 5, 2015
Clothing does not only represent a nation, an era or a prevailing social climate with dierent characteristics,
but it also reflects changes of human civilization. From an emphasis on the natural beauty of the classical
style to themodern or smart clothing in the garment development
ofmodels that are not identiable only from forced responses. Explicit
formulations and an algorithm are derived to identify model parameters from the combined data of forced
and initial condition responses.
Keywords: Linear time-invariant systems, parameter estimation, forced response, initial condition response
MSC 2010: 34A30, 34A55, 93A30, 93B30, 93C05, 65F05
Ya Guo, Jinglu Tan: Department of Bioengineering, University of Missouri, Columbia, MO 65211, USA,
e-mail: email@example.com, firstname.lastname@example.org
Many systems in physics such as wave propagation
Inverse problems for differential pencils with nonlocal conditions are considered.
Uniqueness theorems of inverse problems from the Weyl-type function and spectra
are proved, which are generalizations of the well-known Weyl function and Borg’s inverse
problem for the classical Sturm–Liouville operators.
We consider the boundary value problem :
with and . Motivated by the
previous work [T. Aktosun and V. G. Papanicolaou,
Reconstruction of the wave speed from transmission eigenvalues for the spherically symmetric variable-speed wave equation,
Inverse Problems 29 2013, 6, Article ID 065007], it is natural to consider the following interesting question:
how does one characterize isospectral sets corresponding to problem
In this paper applying constructive methods we answer the above
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.
We give a short review of results on inverse spectral problems for second-order differential operators on an interval with non-separated boundary conditions.
We pay the main attention to the most important nonlinear inverse problems of recovering coefficients of differential operators from given spectral characteristics.
In the first part of the review, we provide the main results and methods related to inverse problems for Sturm–Liouville operators with non-separated boundary conditions: periodic, quasi-periodic and Robin-type boundary conditions.
At the end, we present the main results on inverse problems for differential pencils with non-separated boundary conditions.