The Gronwall inequality for modified Stieltjes integrals
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- by Wayne W. Schmaedeke and George R. Sell
- Proc. Amer. Math. Soc. 19 (1968), 1217-1222
- DOI: https://doi.org/10.1090/S0002-9939-1968-0230864-8
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References
- Lamberto Cesari, Asymptotic behavior and stability problems in ordinary differential equations, 2nd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 16, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963. MR 0151677
- Ralph E. Lane, The integral of a function with respect to a function, Proc. Amer. Math. Soc. 5 (1954), 59–66. MR 59346, DOI 10.1090/S0002-9939-1954-0059346-3
- T. H. Hildebrandt, Definitions of Stieltjes Integrals of the Riemann Type, Amer. Math. Monthly 45 (1938), no. 5, 265–278. MR 1524276, DOI 10.2307/2302540
- H. S. Kaltenborn, Linear functional operations on functions having discontinuities of the first kind, Bull. Amer. Math. Soc. 40 (1934), no. 10, 702–708. MR 1562957, DOI 10.1090/S0002-9904-1934-05949-4 W. W. Schmaedeke, Optimal control of nonlinear differential equations in which the control enters linearly, J. Optimization Theory (to appear). W. W. Schmaedeke and G. R. Sell, On the existence, uniqueness and continuity of solutions of nonlinear Stieltjes integral equations, (to appear).
Bibliographic Information
- © Copyright 1968 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 19 (1968), 1217-1222
- MSC: Primary 26.70
- DOI: https://doi.org/10.1090/S0002-9939-1968-0230864-8
- MathSciNet review: 0230864