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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.

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  • [1] L. È. Èl'sgol'c, Equations with retarded argument which are similar to Euler's equation, Trudy Sem. Teor. Differencial. Uravneniĭ s Otklon. Argumentom Univ. Družby Narodov Patrisa Lumumby 1 (1962), 120. (Russian) MR 32 #2699. 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 39 #3118. MR 0241779 (39:3118)
  • [4] D. I. Martynjuk, Integration by means of series of linear differential equations with deviating argument, Ukrain. Mat. Ž. 18 (1966), no. 5, 105-111. (Russian) MR 34 #458. MR 0200567 (34:458)
  • [5] S. B. Norkin, Differential equations of second order with retarded arguments. Some problems of the theory of vibrations of systems with retardation, ``Nauka", Moscow, 1965; English transl., Transl. Math. Monographs, vol. 31, Amer. Math. Soc., Providence, R.I., 1972. MR 33 #7656. MR 0344628 (49:9367)
  • [6] K. Schmitt, On solutions of nonlinear differential equations with deviating arguments, SIAM J. Appl. Math. 17 (1969), 1171-1176. MR 41 #8782. MR 0264186 (41:8782)

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Keywords: Singular points, neutral differential equations, analytic solutions
Article copyright: © Copyright 1972 American Mathematical Society

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