On the existence of solutions to boundary value problems on time scales

Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

Volumn 12, Issue 5, 2005, Pages 595-606

  Tisdell, Christopher C ^a   Thompson, H B ^b  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

^b UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

Boundary value problem; Dynamic equation; Measure chain; Time scale; Topological degree

Indexed keywords

EID: 26444565362     PISSN: 12013390     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (15)

1. Ravi P. Agarwal, Martin Bohner and Donal O'Regan, Time Scale Boundary Value Problems on Infinite Intervais, J. Comput. Appl. Math., 141 (2002), 27-34.
2. Ravi P. Agarwal and Donal O'Regan, Nonlinear Boundary Value Problems on Time Scales, Nonlinear Analysis, 44 (2001), 527-535.
3. Ravi P. Agarwal, Martin Bohner, Donal O'Regan and Allan Peterson, Dynamic Equations on Time Scales: A Survey, J. Comput. Appl. Math., 141 (2002), 1-26.
4. Elvan Akin, Boundary Value Problems for a Differential Equation on a Measure Chain, Panamer. Math. J., 10 (2000), 17-30.
5. Martin Bohner and Allan Peterson, Dynamic Equations on Time Scales, Birkhauser, Boston, 2001.
6. Lynn Erbe and Allan Peterson, Green's Functions and Comparison Theorems for Differential Equations of Measure Chains, Dynam. Contin. Discrete Impuls. Systems, 6 (1999), 121-137.
7. Lynn Erbe, Allan Peterson and Ronald Mathsen, Existence, Multiplicity and Nonexistence of Positive Solutions to a Differential Equation on a Measure Chain, J. Comput. Appl. Math., 113 (2000), 365-380.
8. T. Gnana Bhaskar, Comparison Theorem for a Nonlinear Boundary Value Problem on Time Scales, J. Comput. Appl. Math., 141 (2002), 117-122.
9. Philip Hartman, Ordinary Differential Equations, John Wiley & Sons, New York, 1964.
10. Johnny Henderson and H. B. Thompson, Difference Equations Associated with Boundary Value Problems for Second Order Nonlinear Ordinary Differential Equations, J. Differ. Equations Appl., 7 (2001), 297-321.
11. Stefan Hilger, Analysis on Measure Chains - A Unified Approach to Continuous and Discrete Calculus, Res. Math., 18 (1990), 18-56.
12. B. Kaymakcalan, Existence and Comparison Results for Dynamic Systems on a Time Scale, J. Math. Anal. Appl., 172 (1993), 243-255.
13. B. Kaymakcalan, V. Lakshmikantham and S. Sivasudaram, Dynamical Systems Measure Chains, Kluwer Academic Publishers, Boston, 1996.
14. N. G. Lloyd, Degree Theory, Cambridge University Press, London, 1978.
15. H. B. Thompson, Second Order Ordinary Differential Equations With Fully Non-linear Two Point Boundary Conditions, Pacific J. Math., 172 (1996), 255-277.