Generalized formulation of the boundary condition for the Liouville equation and for the BBGKY hierarchy

1972 ◽  
Vol 13 (3) ◽  
pp. 1229-1238 ◽  
Author(s):  
D. N. Zubarev ◽  
M. Yu. Novikov
Keyword(s):  
Boundary Condition ◽  
Liouville Equation ◽  
Bbgky Hierarchy

scholarly journals Isospectral sets for boundary value problems on the unit interval

1988 ◽  
Vol 8 (8) ◽  
pp. 301-358 ◽  
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Liouville Equation ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Unit Interval ◽  
Trace Function ◽  
Sturm Liouville ◽  
Real Self

AbstractWe analyse isospectral sets of potentials associated to a given ‘generalized periodic’ boundary condition in SL(2, R) for the Sturm-Liouville equation on the unit interval. This is done by first studying the larger manifold M of all pairs of boundary conditions and potentials with a given spectrum and characterizing the critical points of the map from M to the trace a + d Isospectral sets appear as slices of M whose geometry is determined by the critical point structure of the trace function. This paper completes the classification of isospectral sets for all real self-adjoint boundary conditions.

scholarly journals Inverse problems for the Sturm–Liouville equation with a spectral parameter in the boundary condition

2017 ◽  
Author(s):  
Namig J. Guliyev
Keyword(s):  
Boundary Condition ◽  
Inverse Problems ◽  
Boundary Conditions ◽  
Spectral Parameter ◽  
Liouville Equation ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Eigenvalue Parameter ◽  
Sturm Liouville ◽  
Necessary And Sufficient

Inverse problems of recovering the coefficients of Sturm--Liouville problems with the eigenvalue parameter linearly contained in one of the boundary conditions are studied: (1) from the sequences of eigenvalues and norming constants; (2) from two spectra. Necessary and sufficient conditions for the solvability of these inverse problems are obtained.

scholarly journals An application of comparison criteria to fractional spectral problem having Coloumb potential

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 79-85 ◽  
Author(s):  
Erdal Bas ◽  
Turk Metin
Keyword(s):  
Boundary Condition ◽  
Spectral Problem ◽  
Spectral Theory ◽  
Liouville Equation ◽  
Coulomb Potential ◽  
Liouville Problem ◽  
Comparison Theorems ◽  
Liouville Theory ◽  
Sturm Liouville ◽  
Comparison Criteria

In this study, the zeros of eigen functions of spectral theory are considered in fractional Sturm-Liouville problem. The 1st and 2nd comparison theorems for fractional Sturm-Liouville equation with boundary condition and their proofs are given. In this way, our new approximation will contribute to construct fractional Sturm-Liouville theory. Also, its an application is given in case of Coulomb potential and the results are presented by a symbolic graph.

scholarly journals Lack of Plasma-like Screening Mechanism in Sedimentation of a Non-Brownian Suspension

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 63
Author(s):  
Paweł Sznajder ◽  
Bogdan Cichocki ◽  
Maria Ekiel-Jeżewska
Keyword(s):  
Long Range ◽  
Stationary State ◽  
Liouville Equation ◽  
Correlation Functions ◽  
Bbgky Hierarchy ◽  
Uniform Structure ◽  
Translational Symmetry ◽  
Velocity Fluctuations

We investigate qualitatively a uniform non-Brownian sedimenting suspension in a stationary state. As a base of our analysis we take the BBGKY hierarchy derived from the Liouville equation. We then show that assumption of the plasma-like screening relations can cancel some long-range terms in the hierarchy but it does not provide integrable solutions for correlation functions. This suggests breaking the translational symmetry of the system. Therefore a non-uniform structure can develop to suppress velocity fluctuations and make the range of correlations finite.

scholarly journals Inverse nodal problem for p−Laplacian Bessel equation with polynomially dependent spectral parameter

2018 ◽  
Vol 51 (1) ◽  
pp. 255-263
Author(s):  
Emrah Yilmaz ◽  
Mudhafar Hamadamen ◽  
Tuba Gulsen
Keyword(s):  
Boundary Condition ◽  
Liouville Equation ◽  
Reconstruction Formula ◽  
Bessel Equation ◽  
Inverse Nodal Problem ◽  
Laplacian Energy ◽  
Sturm Liouville ◽  
Nodal Problem ◽  
Energy Dependent ◽  
Prüfer Substitution

Abstract In this study, solution of inverse nodal problem for p−Laplacian Bessel equation is extended to the case that boundary condition depends on polynomial eigenparameter. To find spectral datas as eigenvalues and nodal parameters of this problem, we used a modified Prüfer substitution. Then, reconstruction formula of the potential functions is also obtained by using nodal lenghts. However, this method is similar to used in [Koyunbakan H., Inverse nodal problem for p−Laplacian energy-dependent Sturm-Liouville equation, Bound. Value Probl., 2013, 2013:272, 1-8], our results are more general.

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