Topological transversality and boundary value problems on time scales

Journal of Mathematical Analysis and Applications

Volumn 289, Issue 1, 2004, Pages 110-125

  Henderson, Johnny ^a   Tisdell, Christopher C ^b  

^a BAYLOR UNIVERSITY   (United States)

^b UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Boundary value problem; Time scale; Topological transversality

Indexed keywords

EID: 0346946903     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2003.08.030     Document Type: Article

References (17)

1. R.P. Agarwal, M. Bohner, D. O'Regan, Time scale boundary value problems on infinite intervals, J. Comput. Appl. Math. 141 (2002) 27-34.
2. R.P. Agarwal, D. O'Regan, Nonlinear boundary value problems on time scales, Nonlinear Anal. 44 (2001) 527-535.
3. R.P. Agarwal, M. Bohner, D. O'Regan, A. Peterson, Dynamic equations on time scales: a survey, J. Comput. Appl. Math. 141 (2002) 1-26.
4. E. Akin, Boundary value problems for a differential equation on a measure chain, Panamer. Math. J. 10 (2000) 17-30.
5. M. Bohner, A. Peterson, Dynamic Equations on Time Scales, Birkhauser, Boston, 2001.
6. M. Bohner, A. Peterson (Eds.), Advances in Dynamic Equations on Time Scales, Birkhauser, Boston, 2003.
7. P. Eloe, J. Henderson, Nonlinear boundary value problems and a priori bounds on solutions, SIAM J. Math. Anal. 15 (1984) 642-647.
8. L. Erbe, A. Peterson, Green's functions and comparison theorems for differential equations of measure chains, Dynam. Contin. Discrete Impuls. Systems 6 (1999) 121-137.
9. L. Erbe, A. Peterson, R. Mathsen, Existence, multiplicity and nonexistence of positive solutions to a differential equation on a measure chain, J. Comput. Appl. Math. 113 (2000) 365-380.
10. T.G. Bhaskar, Comparison theorem for a nonlinear boundary value problem on time scales, J. Comput. Appl. Math. 141 (2002) 117-122.
11. A. Granas, Sur la method de continuite de Poincare, C. R. Acad. Sci. Paris 282 (1976) 983-985.
12. A. Granas, R. Guenther, J. Lee, Nonlinear boundary value problems for ordinary differential equations, Dissertationes Math. (Rozprawy Mat.) 244 (1985).
13. J. Henderson, 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.
14. S. Hilger, Analysis on measure chains - a unified approach to continuous and discrete calculus, Res. Math. 18 (1990) 18-56.
15. B. Kaymakcalan, Existence and comparison results for dynamic systems on a time scale, J. Math. Anal. Appl. 172 (1993) 243-255.
16. B. Kaymakcalan, V. Lakshmikantham, S. Sivasudaram, Dynamical Systems on Measure Chains, Kluwer Academic, Boston, 1996.
17. J.A. Pennline, Constructive existence and uniqueness theorems for two-point boundary value problems with a linear gradient term, Appl. Math. Comput. 16 (1984) 233-260.