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Nonlinear integral equations in a measure space


Author: P. C. Das
Journal: Proc. Amer. Math. Soc. 42 (1974), 181-185
MSC: Primary 45G99
DOI: https://doi.org/10.1090/S0002-9939-1974-0326324-9
MathSciNet review: 0326324
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Abstract: An abstract nonlinear integral equation is formulated in a measure space and existence, uniqueness of its solution is proved. It is shown that it includes as particular cases certain classes of integral equations and also differential equations containing measures.


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

  • [1] P. C. Das, Existence of solutions of differential equation approach, An. Sti. Univ. ``Al. I. Cuza'' Iasi Sect. I a Mat. 17 (1971), 53-59. MR 0313610 (47:2164)
  • [2] P. C. Das and R. R. Sharma, On optimal controls for measure delay differential equations, SIAM. J. Control 9 (1971), 43-61. MR 43 #656. MR 0274898 (43:656)
  • [3] 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)
  • [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 32 #7288. MR 0189870 (32:7288)
  • [5] R. R. Sharma, An abstract measure differential equation, Proc. Amer. Math. Soc. 32 (1972), 503-510. MR 45 #691. MR 0291600 (45:691)
  • [6] R. R. Sharma and P. C. Das, Existence and stability of measure differential equations, Czechoslovak Math. J. 22 (97) (1972), 145-158. MR 0304815 (46:3947)

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DOI: https://doi.org/10.1090/S0002-9939-1974-0326324-9
Article copyright: © Copyright 1974 American Mathematical Society

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