scholarly journals On reducibility of linear De-system with constant coefficients on the diagonal to De-system with Jordan matrix in the case of equivalence of its higher order one equation

2016 ◽  
Vol 84 (4) ◽  
pp. 88-93
Author(s):  
A.A. Kulzhumiyeva ◽  
◽  
Zh.A. Sartabanov ◽  
Keyword(s):  
Higher Order ◽  
Constant Coefficients ◽  
Jordan Matrix

scholarly journals Completeness Theorems for Elliptic Equations of Higher Order with Constant Coefficients

2007 ◽  
Vol 14 (1) ◽  
pp. 81-97
Author(s):  
Alberto Cialdea
Keyword(s):  
Elliptic Equation ◽  
Bounded Domain ◽  
Elliptic Equations ◽  
Complete System ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Polynomial Solutions ◽  
Constant Coefficients ◽  
Necessary And Sufficient ◽  
Completeness Theorems

Abstract Let {ω𝑘 } be a complete system of polynomial solutions of the elliptic equation ∑|α|⩽2𝑚 aα 𝐷 α 𝑢 = 0, aα being real constants. We give necessary and sufficient conditions for the completeness of the system in [𝐿𝑝(∂Ω)]𝑚, where Ω ⊂ is a bounded domain such that is connected and ∂Ω ∈ 𝐶1.

HIGHER-ORDER GEODESIC DEVIATIONS AND THE CALCULUS OF RELATIVISTIC ORBITS

2002 ◽  
Vol 17 (20) ◽  
pp. 2756-2756 ◽  
Author(s):  
R. COLISTETE
Keyword(s):  
Harmonic Oscillator ◽  
Taylor Series ◽  
Gravitational Radiation ◽  
Circular Orbit ◽  
Linear Equations ◽  
Higher Order ◽  
Test Particles ◽  
Oscillator Type ◽  
Constant Coefficients ◽  
Systems Of Linear Equations

Starting with an exact and simple geodesic, we generate approximate geodesics1,2 by summing up higher-order geodesic deviations in a fully relativistic scheme. We apply this method to the problem of orbit motion of test particles in Schwarzschild3 and Kerr metrics; from a simple circular orbit as the initial geodesic we obtain finite eccentricity orbits as a Taylor series with respect to the eccentricity. The explicit expressions of these higher-order geodesic deviations are derived using successive systems of linear equations with constant coefficients, whose solutions are of harmonic oscillator type. This scheme is best adapted for small eccentricities, but arbitrary values of M/R. We also analyse the possible application to the calculation of the emission of gravitational radiation from non-circular orbits around a very massive body3.

COMPLETENESS THEOREMS IN THE UNIFORM NORM CONNECTED TO ELLIPTIC EQUATIONS OF HIGHER ORDER WITH CONSTANT COEFFICIENTS

2012 ◽  
Vol 10 (01) ◽  
pp. 1-20 ◽  
Author(s):  
A. CIALDEA
Keyword(s):  
Differential Operator ◽  
Elliptic Equation ◽  
Bounded Domain ◽  
Characteristic Polynomial ◽  
Elliptic Equations ◽  
Uniform Norm ◽  
Normal Derivative ◽  
Higher Order ◽  
Constant Coefficients ◽  
Completeness Theorems

We consider the problem of the completeness of the system [Formula: see text] in [C0(Σ)]m, where {ωk} is a basis of polynomial solutions of the elliptic equation ∑|α|≤2m aαDαu = 0, aα are real constants, Σ is the boundary of a bounded domain in ℝn and ∂ν denotes the normal derivative. If E satisfies a Gårding inequality and [Formula: see text] is connected, we show that such a completeness property holds if and only if all the irreducible factors of the characteristic polynomial of the differential operator vanish at the origin. The proof hinges on some jump formulas obtained for general potentials generated by measures.

scholarly journals Matrix of coefficients for the differential equation of Chauchy-Euler

2018 ◽  
Vol 1 (2) ◽  
pp. 209-213
Author(s):  
Fabio Hernando Castellanos-Moreno ◽  
Jaime Francisco Pantoja-Benavides
Keyword(s):  
Differential Equation ◽  
Higher Order ◽  
Matrix Form ◽  
Characteristic Polynomials ◽  
Or Methodology ◽  
Constant Coefficients ◽  
Novel Methods

In this article application and advance is given to the method that allows to find in a simple way the constant coefficients that are required in the solution of a differential equation with the structure of Cauchy-Euler, presented and made known in [1]. Here we will see the construction form of the characteristic polynomials, using the aforementioned method as a basis; with a series of equations, matrices and novel methods to solve this type of ODEs and, above all, very practical for the equation of a much higher order. The idea is to present a structure or methodology in matrix form that allows to solve in a practical way differential equation of higher order with Cauchy-Euler structure.

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