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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Analytic solutions of a neutral differential equation near a singular point
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by L. J. Grimm PDF
Proc. Amer. Math. Soc. 36 (1972), 187-190 Request permission

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
  • L. È. Èl′sgol′c, Equations with retarded argument which are similar to Euler’s equations, Trudy Sem. Teor. Differencial. Uravneniĭ s Otklon. Argumentom Univ. Družby Narodov Patrisa Lumumby 1 (1962), 120 (Russian). MR 0185230
  • L. J. Grimm, On holomorphic solutions for functional and functional differential equations, Proc. Ninth Internat. Sympos. on Functional Equations, Rome, Italy, 1971.
  • È. I. Grudo, On the analytic theory of ordinary differential equations with deviating argument, Differencial′nye Uravnenija 5 (1969), 700–711 (Russian). MR 0241779
  • D. Ī. Martynjuk, Integration by means of series of linear differential equations with deviating argument, Ukrain. Mat. Ž. 18 (1966), no. 5, 105–111 (Russian). MR 0200567
  • S. B. Norkin, Differential equations of the second order with retarded argument. Some problems of the theory of vibrations of systems with retardation, Translations of Mathematical Monographs, Vol. 31, American Mathematical Society, Providence, R.I., 1972. Translated from the Russian by L. J. Grimm and K. Schmitt. MR 0344628
  • Klaus Schmitt, On solutions of nonlinear differential equations with deviating arguments, SIAM J. Appl. Math. 17 (1969), 1171–1176. MR 264186, DOI 10.1137/0117108
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 36 (1972), 187-190
  • MSC: Primary 34K05
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0318628-9
  • MathSciNet review: 0318628