Differential and difference calculus - Unified!

Nonlinear Analysis, Theory, Methods and Applications

Volumn 30, Issue 5, 1997, Pages 2683-2694

  Hilger, Stefan ^a  

^a CATHOLIC UNIVERSITY OF EICHSTÄTT INGOLSTADT   (Germany)

Author keywords

Gronwall inequality; Measure chains; Sturmian separation theorem; Time scales; Unification of differential and difference calculus

Indexed keywords

EID: 0001028781     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(96)00204-0     Document Type: Article

References (10)

1. J. Dieudonné, Foundations of Modern Analysis. Prentice Hall, New Jersey, 1966.
2. L. Erbe/S. Hilger, Sturmian Theory on Measure Chains, Differential Equations and Dynamical Systems, Vol. 1 (3) (1993), 223-246.
3. T. Fort, Finite Differences and Difference Equations in the Real Domain, Oxford University Press, London, 1948.
4. S. Hilger, Analysis on Measure Chains - A Unified Approach to Continuous and Discrete Calculus, Res. in Math. 18 (1990), 18-56.
5. S. Hilger, Smoothness of Invariant Manifolds, J. Func. Anal. 106 (1992), 95-129.
6. S. Hilger, Generalized Theorem of Hartman-Grobman on Measure Chains, J. Austral. Math. Soc., Series A, 60 (1996), 157-191.
7. S. Hilger, P.E. Kloeden, Vlijanie vremennoj zernistosti na asimptoticeskuju ustojcivost' dinamiceskich sistem, Avtomatica i telemechanica, Jg. 1994, H. 9, S. 68-74. (Comparative time grainyness and asymptotic stability of dynamical equations).
8. V. Lakshmikantham/D. Trigiante, Theory of Difference Equations, Academic Press, Inc., San Diego 1988.
9. A.B. Mingarelli, Volterra-Stieltjes Integral Equations and Generalized Ordinary Differential Expressions, Lecture Notes in Mathematics 989, Springer, Berlin-Heidelberg-New York-Tokyo, 1983.
10. J. Popenda, On the Systems of Discrete Inequalities of Gronwall Type, JMAA 183, 663-669 (1994).