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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Analytic solutions of a neutral differential equation near a singular point


Author: L. J. Grimm
Journal: Proc. Amer. Math. Soc. 36 (1972), 187-190
MSC: Primary 34K05
MathSciNet review: 0318628
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Abstract: Fixed point techniques are employed to prove existence and uniqueness of a holomorphic solution to a functional differential equation of neutral type in the neighborhood of a regular singular point.


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

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  • [2] L. J. Grimm, On holomorphic solutions for functional and functional differential equations, Proc. Ninth Internat. Sympos. on Functional Equations, Rome, Italy, 1971.
  • [3] È. I. Grudo, On the analytic theory of ordinary differential equations with deviating argument, Differencial′nye Uravnenija 5 (1969), 700–711 (Russian). MR 0241779 (39 #3118)
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  • [5] S. B. Norkin, Differential equations of the second order with retarded argument. Some problems of the theory of vibrations of systems with retardation, American Mathematical Society, Providence, R.I., 1972. Translated from the Russian by L. J. Grimm and K. Schmitt; Translations of Mathematical Monographs, Vol. 31. MR 0344628 (49 #9367)
  • [6] Klaus Schmitt, On solutions of nonlinear differential equations with deviating arguments, SIAM J. Appl. Math. 17 (1969), 1171–1176. MR 0264186 (41 #8782)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0318628-9
PII: S 0002-9939(1972)0318628-9
Keywords: Singular points, neutral differential equations, analytic solutions
Article copyright: © Copyright 1972 American Mathematical Society