Smoothness of solutions of conjugate boundary-value problems on a measure chain

Electronic Journal of Differential Equations

Volumn 2000, Issue , 2000, Pages

  Kaufmann, Eric R ^a  

^a University of Arkansas at Little Rock ^*  (United States)

Author keywords

Boundary value problem; Initial value problem; Measure chain

Indexed keywords

EID: 0742299845     PISSN: 10726691     EISSN: 10726691     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. R. P. Agarwal and M. Bohner, Basic calculus on time scales and some of its applications, Results Math. 35 (1999), 3 - 22.
2. D. Anderson, Positivity of Green's functions for ri-point right focal boundary-value proble on a measure chain, preprint.
3. B. Aulback and S. Hilger, Linear dynamic processes with inhomogeneous time scale, Nonlinea Dynamics and Quantum Dynamical Systems, Math. Res. 59, Akademie Verlag, Berlin, 1990.
4. C. J. Chyan, J.M. Davis, J. Henderson and W.K.C.Yin, Eigenvalue comparisons for differentia equations on a Measure Chain, Electronic Jour. Diff. Equns. 35(1998), 1-7.
5. A. Datta and J. Henderson, Differentiation of solutions of difference equations with respec to right focal boundary values, PanAmer. Math. J. 2 (1992), 1 - 16.
6. J. Ehme, and D. Brewley, Continuous Data Dependence for a Class of Nonlinear Boundar Value Problems, Comm. Appl. Nonlinear Anal, 3 (1996) No. 2, 59-65.
7. J. Ehme and J. Henderson, Differentiation of solutions of boundary-value problems wit respect to boundary conditions, Appl. Anal. 46 (1992), 175 - 194.
8. L.H. Erbe and S. Hilger, Sturmian theory on measure chains, Differential Equations Dynam. Systems 1(1993), 223-246.
9. L.H. Erbe and A. Peterson, Green's functions and comparison theorems for differential equations on measure chains, Dynam. Contin. Discrete Impuls. Systems, 6 (1999), 121 - 137.
10. L.H. Erbe and A. Peterson, Positive solutions for a nonlinear differential equation on a measure chain, preprint.
11. D. Hankerson, Boundary Value Problems for nth Order Difference Equations, Ph.D. dissertation, University of Nebraska-Lincoln, 1986.
12. P. Hartman, Difference equations: disconjugacy, principal solutions, Green's functions, complete monotonicity, Trans. Amer. Math. Soc. 246 (1978), l - 30.
13. J. Henderson, Disconjugacy, disfocality, and differentiation with respect to boundary conditions, J. Math. Anal. Appl. 121 No. l (1987), l - 9.
14. J. Henderson, M. Horn and L. Howard, Differentiation of soltuions with respect to boundar values and parameters, Comm. Appl. Nordin. Anal. 1 (1994), 47-60.
15. J. Henderson and E. R. Kaufmann, Multipoint boundary value problems with parameter for a system of difference equations, Journal of Difference Equations and Applications, 1 (1995), 163-172.
16. J. Henderson and L. Lee, Continuous dependence and differentiation of solutions of finit difference equations, Internat. J. Math, and Math. Sci. 14 No. 4 (1991), 747 - 756.
17. S. Hilger, Analysis on measure chains - a unified approach to continuous and discrete calculus, Results Math. 18(1990), 18-56.
18. V. Lakshmikantham, B. Kaymakcalan and S. Sivasundaram, Dynamical Systems on Measure Chains, Kluwer Academic Publishers, Boston, 1996.
19. A. C. Peterson, Comparison theorems and existence theorems for ordinary differential equations, J. Math. Anal. Appl. 55 No. 3 (1976), 773-784.