Oscillation Criteria for Matrix Differential Inequalities(1)

1973 ◽  
Vol 16 (1) ◽  
pp. 5-10 ◽  
Author(s):  
W. Allegretto ◽  
L. Erbe
Keyword(s):  
Differential Equation ◽  
Sufficient Conditions ◽  
Positive Semidefinite ◽  
Matrix Functions ◽  
Differential Inequalities ◽  
Matrix Differential Equation ◽  
Oscillation Criteria ◽  
Matrix Differential ◽  
Image Position

Several authors have recently considered the problem of obtaining sufficient conditions for the oscillation of the quasilinear matrix differential equation(1)and the associated inequality VTLV ≤ 0 (as a form). Here A, B, and V are m x m matrix functions, A(x) is symmetric, positive semidefinite and continuous in an interval [a, ∞) and B(x,V, V') is symmetric and continuous in a≤ x < ∞ for all V and V'.

scholarly journals Some Results On The Asymptotic Behavior Of Linear Systems

1955 ◽  
Vol 7 ◽  
pp. 531-538 ◽  
Author(s):  
M. Marcus
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Matrix Differential Equation ◽  
Complex Matrix ◽  
Continuous Complex ◽  
Matrix Differential ◽  
Image Position ◽  
Vector Matrix ◽  
Complex Valued ◽  
Square Complex

1. Introduction. We consider first in §2 the asymptotic behavior as t → ∞ of the solutions of the vector-matrix differential equation(1.1) ,where A is a constant n-square complex matrix, B{t) a continuous complex valued n-square matrix defined on [0, ∞ ), and x a complex n-vector.

A Converse Problem in Matrix Differential Equations

1973 ◽  
Vol 16 (3) ◽  
pp. 401-403
Author(s):  
Warren E. Shreveo
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Matrix Differential Equation ◽  
Converse Problem ◽  
Matrix Differential Equations ◽  
Matrix Differential ◽  
Image Position

Suppose X and F are nxn matrix solutions of the n X n matrix differential equation(1)such that(2)where J is some interval.

scholarly journals Modified Laguerre matrix polynomials

Filomat ◽  
2014 ◽  
Vol 28 (10) ◽  
pp. 2069-2076 ◽  
Author(s):  
Levent Kargin ◽  
Veli Kurt
Keyword(s):  
Differential Equation ◽  
Explicit Expression ◽  
Matrix Functions ◽  
Series Solutions ◽  
Matrix Differential Equation ◽  
Rodrigues Formula ◽  
Matrix Polynomials ◽  
Generating Matrix Functions ◽  
Generating Matrix ◽  
Matrix Differential

In this paper, modified Laguerre matrix polynomials which appear as finite series solutions of second-order matrix differential equation are introduced. Some formulas related to an explicit expression, a three-term matrix recurrence relation and a Rodrigues formula are obtained. Several families of bilinear and bilateral generating matrix functions for modified Laguerre matrix polynomials are derived. Finally a new generalization of the Laguerre-type matrix polynomials is introduced.

scholarly journals ON CONDITIONING FOR A GENERAL SYSTEM OF FOUR POINT BOUNDARY VALUE PROBLEMS

1996 ◽  
Vol 27 (3) ◽  
pp. 219-225
Author(s):  
M. S. N. MURTY
Keyword(s):  
Differential Equation ◽  
Fundamental Matrix ◽  
Close Relationships ◽  
General System ◽  
Point Boundary ◽  
Matrix Differential Equation ◽  
Growth Behaviour ◽  
First Order ◽  
Matrix Differential ◽  
The Stability

In this paper we investigate the close relationships between the stability constants and the growth behaviour of the fundamental matrix to the general FPBVP'S associated with the general first order matrix differential equation.

scholarly journals Oscillation Criteria for Second Order Neutral Differential Equations

1996 ◽  
Vol 48 (4) ◽  
pp. 871-886 ◽  
Author(s):  
Horng-Jaan Li ◽  
Wei-Ling Liu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Second Order ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Neutral Delay Differential Equation ◽  
Image Position ◽  
Delay Differential

AbstractSome oscillation criteria are given for the second order neutral delay differential equationwhere τ and σ are nonnegative constants, . These results generalize and improve some known results about both neutral and delay differential equations.

On Stability of Solutions of Certain Differential Equations of the Third Order

1967 ◽  
Vol 10 (5) ◽  
pp. 681-688 ◽  
Author(s):  
B.S. Lalli
Keyword(s):  
Differential Equation ◽  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Differential Equations ◽  
Global Asymptotic Stability ◽  
Sufficient Conditions ◽  
Stability Of Solutions ◽  
Third Order ◽  
The Third ◽  
Image Position

The purpose of this paper is to obtain a set of sufficient conditions for “global asymptotic stability” of the trivial solution x = 0 of the differential equation1.1using a Lyapunov function which is substantially different from similar functions used in [2], [3] and [4], for similar differential equations. The functions f1, f2 and f3 are real - valued and are smooth enough to ensure the existence of the solutions of (1.1) on [0, ∞). The dot indicates differentiation with respect to t. We are taking a and b to be some positive parameters.

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