First order difference system-

existence and uniqueness

Authors:
K. N. Murty, P. V. S. Anand and V. Lakshmi Prasannam

Journal:
Proc. Amer. Math. Soc. **125** (1997), 3533-3539

MSC (1991):
Primary 39A10, 34B05

DOI:
https://doi.org/10.1090/S0002-9939-97-04250-0

MathSciNet review:
1443846

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, the general solution of the homogeneous matrix difference system is constructed in terms of two fundamental matrix solutions. The general solution of the inhomogeneous matrix difference system is established by the variation of parameters formula. A unique solution of the two-point boundary value problem associated with the matrix difference system is constructed by applying the QR-algorithm and the Bartels-Stewart algorithm.

**1.**Ravi P. Agarwal,*On multi-point boundary value problems for discrete equations*, J. Math. Anal.**96(2)**(1983), 520-534. MR**84k:39001****2.**V. Lakshmikantham and D. Trigiante,*Theory of difference equations*:*Numerical methods and applications*, Academic Press, 1988. MR**89g:39003****3.**F. V. Atkinson,*Discrete and continuous boundary value problems*, Academic Press, New York, 1964. MR**31:416****4.**A. Jameson,*Solution of the equation by inversion of an or matrix*, SIAM J. Appl. Math.**16(5)**1968, 1010-1023. MR**38:3286****5.**P. Lancaster,*Explicit solutions of linear matrix equations*, SIAM Review**12(4)**, 1970, 544-566. MR**43:4841****6.**G. W. Stewart and R. H. Bartels,*A solution of the equation*, Common. ACM**15**, 1976, 820-826.**7.**K. N. Murty, K. R. Prasad and P. V. S. Anand,*Two-point boundary value problems associated with Liapunov type matrix difference system*, Dynam. Systems Appl.**4**(1995), 205-213. CMP**95:14**

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Additional Information

**K. N. Murty**

Affiliation:
Department of Applied Mathematics, Andhra University, Visakhapatnam - 530 003, India

**V. Lakshmi Prasannam**

Affiliation:
Department of Mathematics, Post Graduate Centre, P. B. Siddhartha College Of Arts & Science, Vijayawada - 520 010, India

DOI:
https://doi.org/10.1090/S0002-9939-97-04250-0

Received by editor(s):
April 17, 1996

Communicated by:
Hal L. Smith

Article copyright:
© Copyright 1997
American Mathematical Society