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 Fundamental systems and solutions of nonhomogeneous equations for a pair of mixed linear ordinary differential equations

1990 ◽  
Vol 49 (1) ◽  
pp. 161-173
Author(s):  
M. Venkatesulu ◽  
T. Gnana Bhaskar
Keyword(s):  
Differential Equations ◽  
Systematic Study ◽  
Differential Operators ◽  
Linear Ordinary Differential Equations ◽  
Physical Conditions ◽  
Transverse Vibrations ◽  
Ordinary Differential Operators ◽  
Acoustic Waveguides ◽  
Complete Set ◽  
Fundamental Systems

AbstractTwo different ordinary differential operators L1 and L2 (not of the same order) defined on two adjacent intervals I1 and I2, respectively, with certain mixed conditions at the interface are considered. These problems are encountered in the study of ‘acoustic waveguides in ocean’, ‘transverse vibrations in nonhomogeneous strings’, etc. A complete set of physical conditions on the system give rise to three types of (selfadjoint) boundary value problems associated with the pair (L1, L2). In a series of papers, a systematic study of these new classes of problems is being developed. In the present paper, we construct the fundamental systems and exhibit the forms of solutions of nonhomogeneous problems associated with the pair (L1, L2).

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 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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