Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The Gronwall inequality for modified Stieltjes integrals


Authors: Wayne W. Schmaedeke and George R. Sell
Journal: Proc. Amer. Math. Soc. 19 (1968), 1217-1222
MSC: Primary 26.70
MathSciNet review: 0230864
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  • [1] L. Cesari, Asymptotic behavior and stability problems in ordinary differential equations, 2nd ed., Academic Press, New York, 1963. MR 0151677 (27:1661)
  • [2] R. E. Lane, The integral of a function with respect to a function, Proc. Amer. Math. Soc. 5(1954), 59-66. MR 0059346 (15:514e)
  • [3] T. H. Hildebrandt, Definitions of Stieltjes integrals of the Riemann type, Amer. Math. Monthly 45 (1938), 265-278. MR 1524276
  • [4] H. S. Kaltenborn, Linear functional operations on functions having discontinuities of the first kind, Bull. Amer. Math. Soc. 40 (1934), 702-708. MR 1562957
  • [5] W. W. Schmaedeke, Optimal control of nonlinear differential equations in which the control enters linearly, J. Optimization Theory (to appear).
  • [6] W. W. Schmaedeke and G. R. Sell, On the existence, uniqueness and continuity of solutions of nonlinear Stieltjes integral equations, (to appear).

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DOI: http://dx.doi.org/10.1090/S0002-9939-1968-0230864-8
Article copyright: © Copyright 1968 American Mathematical Society