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.

**[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****[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****[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****[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****[6]**Klaus Schmitt,*On solutions of nonlinear differential equations with deviating arguments*, SIAM J. Appl. Math.**17**(1969), 1171–1176. MR**0264186**

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1972-0318628-9

Keywords:
Singular points,
neutral differential equations,
analytic solutions

Article copyright:
© Copyright 1972
American Mathematical Society