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Existence of solutions of abstract measure differential equations


Author: R. R. Sharma
Journal: Proc. Amer. Math. Soc. 35 (1972), 129-136
MSC: Primary 34G05
DOI: https://doi.org/10.1090/S0002-9939-1972-0304811-5
MathSciNet review: 0304811
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Abstract: In an earlier paper the author has introduced an abstract measure differential equation as a generalization of ordinary differential equations and measure differential equations, and proved a theorem for the existence and uniqueness of solutions of this equation. In the present paper the problem of the existence of solutions is further investigated.


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

  • [1] E. A. Coddingtun and N. Levinson, Theory of ordinary differential equations, McGraw-Hill, New York, 1955. MR 16, 1022. MR 0069338 (16:1022b)
  • [2] N. Dunford and J. T. Schwartz, Linear operators. I: General theory, Pure and Appl. Math., vol. 7, Interscience, New York, 1958. MR 22 #8302. MR 0117523 (22:8302)
  • [3] R. R. Sharma, An abstract measure differential equation, Proc. Amer. Math. Soc. 32 (1972), 503-510. MR 0291600 (45:691)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0304811-5
Keywords: Abstract measure differential equation, real measures, complex measures, Radon-Nikodym derivative, total variation measure, pseudometric
Article copyright: © Copyright 1972 American Mathematical Society

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