Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)

  • [1] 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 (32 #2699)
  • [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)
  • [4] 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 (34 #458)
  • [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)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34K05

Retrieve articles in all journals with MSC: 34K05

Additional Information

PII: S 0002-9939(1972)0318628-9
Keywords: Singular points, neutral differential equations, analytic solutions
Article copyright: © Copyright 1972 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia