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Variation of parameters formula for the equation of Cooke and Wiener

Authors: K. N. Jayasree and S. G. Deo
Journal: Proc. Amer. Math. Soc. 112 (1991), 75-80
MSC: Primary 34K05
MathSciNet review: 1057744
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Abstract: A variation of parameters and Gronwall type integral inequality are proved for a differential equation involving piecewise alternately retarded and advanced argument.

References [Enhancements On Off] (What's this?)

  • [1] S. Busenberg and K. L. Cooke, Models of vertically transmitted diseases with sequential-continuous dynamics, Nonlinear Phenomena in Mathematical Sciences (V. Lakshmikantham, ed.), Academic Press, New York, 1982, pp. 179-187.
  • [2] K. L. Cooke and J. Wiener, Retarded differential equations with piecewise constant delays, J. Math. Anal. Appl. 99 (1984), 265-297. MR 732717 (85d:34072)
  • [3] -, An equation alternately of retarded and advanced type, Proc. Amer. Math. Soc. 99 (1987), 726-732. MR 877047 (88g:34119)
  • [4] J. K. Hale, Theory of functional differential equations, Applied Mathematical Sciences, vol. 3, Springer-Verlag, New York, 1976. MR 0466837 (57:6711)
  • [5] V. Lakshmikantham and S. Leela, Differential and integral inequalities, vol. 1, Academic Press, New York, 1969.

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Keywords: Variation of parameters formula, Gronwall integral inequality, alternately retarded and advanced argument
Article copyright: © Copyright 1991 American Mathematical Society

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