Previous article Next article Fundamental Inequalities for Discrete and Discontinuous Functional EquationsG. Stephen JonesG. Stephen Joneshttps://doi.org/10.1137/0112004PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Tom M. Apostol, Mathematical analysis: a modern approach to advanced calculus, Addison-Wesley Publishing Company, Inc., Reading, Mass., 1957, 191–250 MR0087718 0077.05501 Google Scholar[2] Richard Bellman, Stability theory of differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953xiii+166 MR0061235 0053.24705 Google Scholar[3] Richard Bellman, On the boundedness of solutions of nonlinear differential and difference equations, Trans. Amer. Math. Soc., 62 (1947), 357–386 MR0023996 0031.39901 CrossrefISIGoogle Scholar[4] Richard Bellman, A Survey of the Theory of the Boundedness, Stability, and Asymptotic Behavior of Solutions of Linear and Nonlinear Differential and Difference Equations, Office of Naval Research, Washington, D. C., 1949vi+156, NAVEXOS P-596 MR0030662 Google Scholar[5] Earl A. Coddington and , Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955xii+429 MR0069338 0064.33002 Google Scholar[6] T. H. Gronwall, Note on the derivatives with respect to a parameter of the solutions of a system of differential equations, Ann. of Math. (2), 20 (1919), 292–296 MR1502565 CrossrefGoogle Scholar[7] Peter Henrici, Discrete variable methods in ordinary differential equations, John Wiley & Sons Inc., New York, 1962xi+407 MR0135729 0112.34901 Google Scholar[8] G. Ja. Karasik, On the preservation of a periodic solution in the transition from a differential equation to a finite-difference equation, Naučn. Dokl. Vysš. Skoly Fiz.-Mat. Nauki, 1958 (1958), 43–46 MR0136834 Google Scholar[9] Otis E. Lancaster, Some results concerning the behavior at infinity of real continuous solutions of algebraic difference equations, Bull. Amer. Math. Soc., 46 (1940), 169–177 MR0001108 0022.33803 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails A Discrete Dynamic Programming Approximation to the Multiobjective Deterministic Finite Horizon Optimal Control ProblemSIAM Journal on Control and Optimization, Vol. 48, No. 4 | 4 September 2009AbstractPDF (249 KB)Prediction of Zero Points of Solutions to Lanchester-Type Differential Combat Equations for Modern WarfareSIAM Journal on Applied Mathematics, Vol. 36, No. 3 | 12 July 2006AbstractPDF (1752 KB)$L_p $-Stability of Linear Time-Varying Feedback SystemsSIAM Journal on Control, Vol. 6, No. 2 | 18 July 2006AbstractPDF (581 KB) Volume 12, Issue 1| 1964Journal of the Society for Industrial and Applied Mathematics1-248 History Submitted:30 August 1962Published online:13 July 2006 InformationCopyright © 1964 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0112004Article page range:pp. 43-57ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics