On a functional equation arising in the stability theory of difference-differential equations

Authors:
W. B. Castelan and E. F. Infante

Journal:
Quart. Appl. Math. **35** (1977), 311-319

MSC:
Primary 34K05

DOI:
https://doi.org/10.1090/qam/492694

MathSciNet review:
492694

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Abstract | References | Similar Articles | Additional Information

Abstract: The functional differential equation

**[1]**Richard Bellman,*Introduction to matrix analysis*, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1960. MR**0122820****[2]**Richard Bellman and Kenneth L. Cooke,*Differential-difference equations*, Academic Press, New York-London, 1963. MR**0147745****[3]**Earl A. Coddington and Norman Levinson,*Theory of ordinary differential equations*, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. MR**0069338****[4]**Richard Datko,*An algorithm for computing Liapunov functionals for some differential-difference equations*, Ordinary differential equations (Proc. NRL-MRC Conf., Math. Res. Center, Naval Res. Lab., Washington, D.C., 1971) Academic Press, New York, 1972, pp. 387–398. MR**0454261****[5]**Jack K. Hale,*Ordinary differential equations*, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1969. Pure and Applied Mathematics, Vol. XXI. MR**0419901****[6]**Jack K. Hale,*Functional differential equations*, Analytic theory of differential equations (Proc. Conf., Western Michigan Univ., Kalamazoo, Mich., 1970) Springer, Berlin, 1971, pp. 9–22. Lecture Notes in Mat., Vol. 183. MR**0390425****[7]**Jack Hale,*Theory of functional differential equations*, 2nd ed., Springer-Verlag, New York-Heidelberg, 1977. Applied Mathematical Sciences, Vol. 3. MR**0508721****[8]**E. F. Infante and W. B. Castelan,*A Liapunov functional for a matrix differential difference equation*, to appear**[9]**E. F. Infante and J. A. Walker,*A Liapunov functional for a scalar differential difference equation*, Proc. Roy. Soc. Edinburgh (to appear)**[10]**Peter Lancaster,*Theory of matrices*, Academic Press, New York-London, 1969. MR**0245579****[11]**Iu. M. Repin,*Quadratic Liapunov functionals for systems with delay*, J. Appl. Math. Mech.**29**(1965), 669–672 (1966). MR**0206422**, https://doi.org/10.1016/0021-8928(65)90072-9

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DOI:
https://doi.org/10.1090/qam/492694

Article copyright:
© Copyright 1977
American Mathematical Society