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Proceedings of the American Mathematical Society

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An abstract measure differential equation

Author: R. R. Sharma
Journal: Proc. Amer. Math. Soc. 32 (1972), 503-510
MSC: Primary 34G05
MathSciNet review: 0291600
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Abstract: An abstract measure differential equation is introduced as a generalization of ordinary differential equations and measure differential equations. The existence and extension of solutions of this equation are considered.

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

  • [1] P. C. Das and R. R. Sharma, On optimal controls for measure delay-differential equations, SIAM J. Control 9 (1971), 43–61. MR 0274898
  • [2] Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London, 1958. MR 0117523
  • [3] Walter Rudin, Real and complex analysis, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210528
  • [4] W. W. Schmaedeke, Optimal control theory for nonlinear vector differential equations containing measures, J. Soc. Indust. Appl. Math. Ser. A Control 3 (1965), 231–280. MR 0189870
  • [5] P. C. Das and R. R. Sharma, Existence and stability of measure differential equations, Czechoslovak Math. J. 22(97) (1972), 145–158. MR 0304815

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Keywords: Ordinary differential equations, measure differential equations, complex measure, Radon-Nikodym derivative, function of bounded variation, distributional derivative, total variation measure, principle of contraction mapping, Borel measure, Lebesgue-Stieltjes measure
Article copyright: © Copyright 1972 American Mathematical Society