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The asymptotic behavior of the solutions of linear and nonlinear differential-difference equations


Author: K. L. Cooke
Journal: Trans. Amer. Math. Soc. 75 (1953), 80-105
MSC: Primary 39.0X
DOI: https://doi.org/10.1090/S0002-9947-1953-0060133-4
MathSciNet review: 0060133
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  • [1] R. Bellman, The boundedness of solutions of linear differential equations, Duke Math. J. vol. 14 (1947) pp. 83-97. MR 0021189 (9:35b)
  • [2] -, On the existence and boundedness of solutions of non-linear differential-difference equations, Ann. of Math. vol. 50 (1949) pp. 347-355. MR 0030106 (10:715a)
  • [3] S. Bochner, Allgemeine lineare Differenzgleichungen mit asymptotisch konstanten Koeffizienten, Math. Zeit. vol. 33 (1931) pp. 426-450. MR 1545221
  • [4] F. H. Brownell, Non-linear delay differential equations, "Contributions to the Theory of Non-linear Oscillations," Annals of Mathematics Studies, no. 20, Princeton, 1950, pp. 89-148. MR 0035382 (11:726b)
  • [5] G. Doetsch, Theorie und Anwendung der Laplace-Transformation, New York, 1943. MR 0009225 (5:119f)
  • [6] N. D. Hayes, Roots of the transcendental equation associated with a certain difference-differential equation, J. London Math. Soc. vol. 25 (1950) pp. 226-232. MR 0036426 (12:106d)
  • [7] O. Hilb, Zur Theorie der linearen funktionale Differentialgleichungen, Math. Ann. vol. 78 (1917) pp. 137-170. MR 1511888
  • [8] G. Hoheisel, Randwertaufgaben und funktionale Differentialgleichungen, Jber. Deutschen. Math. Verein. vol. 39 (1930) pp. 54-58.
  • [9] M. Hukuhara, Sur les points singuliers des equations differentielles lineaires, Journal of the Faculty of Science. Hokaido Imperial University Ser. I, vol. 2 (1934) pp. 13-88.
  • [10] H. R. Pitt, On a class of linear integro-differential equations, Proc. Cambridge Philos. Soc. Vol. 40 (1944) pp. 199-211. MR 0012197 (6:273b)
  • [11] E. Schmidt, Über eine Klasse linearer funktionaler Differentialgleichungen, Math. Ann. vol. 70 (1911) pp. 499-524. MR 1511633
  • [12] E. C. Titchmarsh, Solutions of some functional equations, J. London Math. Soc. vol. 14 (1939) pp. 118-124.
  • [13] W. J. Trjitzinsky, Analytic theory of linear differential equations, Acta Math. vol. 62 (1934) pp. 167-226. MR 1555383
  • [14] E. M. Wright, The non-linear difference-differential equation, Quart. J. Math. Oxford Ser. (1) vol. 17 (1946) pp. 245-252. MR 0019207 (8:385a)
  • [15] -, Linear difference-differential equations, Proc. Cambridge Philos Soc. vol. 44 (1948) pp. 179-185. MR 0026230 (10:125c)
  • [16] -, The linear difference-differential equation with asymptotically constant coefficients, Amer. J. Math. vol. 70 (1948) pp. 221-238. MR 0025063 (9:592a)
  • [17] -, The linear difference-differential equation with constant coefficients, Proceedings of the Royal Society of Edinburgh, Sec. A vol. 62 (1949) pp. 387-393. MR 0031639 (11:182d)
  • [18] -, The stability of solutions of non-linear difference-differential equations, Proceedings of the Royal Society of Edinburgh, Sec. A vol. 63 (1950) pp. 18-26. MR 0036425 (12:106c)

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DOI: https://doi.org/10.1090/S0002-9947-1953-0060133-4
Article copyright: © Copyright 1953 American Mathematical Society

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