scholarly journals Book Review: Boundary value problems, Weyl functions, and differential operators

2020 ◽  
Vol 58 (1) ◽  
pp. 129-136
Author(s):  
Fritz Gesztesy
Keyword(s):  
Boundary Value Problems ◽  
Differential Operators ◽  
Boundary Value ◽  
Weyl Functions

Recovering differential operators with two constant delays under Dirichlet/Neumann boundary conditions

2020 ◽  
Vol 28 (2) ◽  
pp. 237-241
Author(s):  
Biljana M. Vojvodic ◽  
Vladimir M. Vladicic
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Differential Operators ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions

AbstractThis paper deals with non-self-adjoint differential operators with two constant delays generated by {-y^{\prime\prime}+q_{1}(x)y(x-\tau_{1})+(-1)^{i}q_{2}(x)y(x-\tau_{2})}, where {\frac{\pi}{3}\leq\tau_{2}<\frac{\pi}{2}<2\tau_{2}\leq\tau_{1}<\pi} and potentials {q_{j}} are real-valued functions, {q_{j}\in L^{2}[0,\pi]}. We will prove that the delays and the potentials are uniquely determined from the spectra of four boundary value problems: two of them under boundary conditions {y(0)=y(\pi)=0} and the remaining two under boundary conditions {y(0)=y^{\prime}(\pi)=0}.

scholarly journals Computation of Green's matrices for boundary value problems associated with a pair of mixed linear regular ordinary differential operators

1995 ◽  
Vol 18 (4) ◽  
pp. 789-797 ◽  
Author(s):  
T. Gnana Bhaskar ◽  
M. Venkatesulu
Keyword(s):  
Boundary Value Problems ◽  
Differential Operators ◽  
Boundary Value ◽  
Transverse Vibrations ◽  
Ordinary Differential Operators ◽  
Acoustic Waveguides

An algorithm for the computation of Green's matrices for boundary value problems associated with a pair of mixed linear regular ordinary differential operators is presented and two examples from the studies of acoustic waveguides in ocean and transverse vibrations in nonhomogeneous strings are discussed.

scholarly journals Degenerate Differential Operators with Parameters

2007 ◽  
Vol 2007 ◽  
pp. 1-27 ◽  
Author(s):  
Veli B. Shakhmurov
Keyword(s):  
Boundary Value Problems ◽  
Differential Operators ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Cylindrical Domain ◽  
Nonlocal Boundary Value Problems ◽  
Degenerate Elliptic ◽  
Systems Of Elliptic Equations ◽  
Principal Parts ◽  
Degenerate Differential Operator

The nonlocal boundary value problems for regular degenerate differential-operator equations with the parameter are studied. The principal parts of the appropriate generated differential operators are non-self-adjoint. Several conditions for the maximal regularity uniformly with respect to the parameter and the Fredholmness in Banach-valuedLp−spaces of these problems are given. In applications, the nonlocal boundary value problems for degenerate elliptic partial differential equations and for systems of elliptic equations with parameters on cylindrical domain are studied.

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