Quadratic functionals for second order matrix equations on time scales

1998 ◽  
Vol 33 (7) ◽  
pp. 675-692 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Martin Bohner
Keyword(s):  
Time Scales ◽  
Second Order ◽  
Matrix Equations ◽  
Quadratic Functionals ◽  
Order Matrix

scholarly journals The Solutions of Second-Order Linear Matrix Equations on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Kefeng Li ◽  
Chao Zhang
Keyword(s):  
Time Scales ◽  
Characteristic Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Matrix ◽  
Matrix Equations ◽  
Existence Of A Solution ◽  
Order Linear ◽  
The Matrix ◽  
Linear Matrix Equations

This paper studies the solutions of second-order linear matrix equations on time scales. Firstly, the necessary and sufficient conditions for the existence of a solution of characteristic equation are introduced; then two diverse solutions of characteristic equation are applied to express general solution of the matrix equations on time scales.

scholarly journals Sturm-Picone comparison theorem for matrix systems on time scales

2010 ◽  
Vol 4 (2) ◽  
pp. 338-346 ◽  
Author(s):  
Douglas Anderson ◽  
John Graef
Keyword(s):  
Time Scales ◽  
Comparison Theorem ◽  
Second Order ◽  
Matrix Equations ◽  
Arbitrary Time ◽  
Dynamic Matrix ◽  
Picone Identity

A well-known Picone identity is extended and generalized to second-order dynamic matrix equations on arbitrary time scales. A comparison theorem is obtained in the spirit of the classical Sturm-Picone comparison theorem that extends known scalar results to matrix equations that include the linear homogeneous and inhomogeneous cases, and nonlinear unperturbed and perturbed cases.

scholarly journals Oscillation Criteria of Singular Initial-Value Problem for Second Order Nonlinear Dynamic Equation on Time Scales

2018 ◽  
Vol 5 (1) ◽  
pp. 102-112 ◽  
Author(s):  
Shekhar Singh Negi ◽  
Syed Abbas ◽  
Muslim Malik
Keyword(s):  
Time Scales ◽  
Initial Value Problem ◽  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Type Inequality ◽  
Second Order ◽  
Oscillation Criterion ◽  
Initial Value ◽  
Nonlinear Dynamic Equation ◽  
Singular Initial Value Problem

AbstractBy using of generalized Opial’s type inequality on time scales, a new oscillation criterion is given for a singular initial-value problem of second-order dynamic equation on time scales. Some oscillatory results of its generalizations are also presented. Example with various time scales is given to illustrate the analytical findings.

scholarly journals A Markovian canonical form of second-order matrix-exponential processes

2008 ◽  
Vol 190 (2) ◽  
pp. 459-477 ◽  
Author(s):  
L. Bodrog ◽  
A. Heindl ◽  
G. Horváth ◽  
M. Telek
Keyword(s):  
Canonical Form ◽  
Second Order ◽  
Matrix Exponential ◽  
Order Matrix
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