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Abstract:

Here, we investigate systems of boundary value problems for dynamic equations on time scales. Using a generalized relationship between the boundary conditions and a certain subset of the solution space, the existence of solutions is established through topological arguments. The main tools used are Leray - Schauder and Brouwer degree theory. © 2004 Elsevier Inc. All rights reserved.

Registro:

Documento: Artículo
Título:Existence of solutions to boundary value problems for dynamic systems on time scales
Autor:Amster, P.; Rogers, C.; Tisdell, C.C.
Filiación:Departamento de Matemática, Universidad de Buenos Aires, CONICET, Buenos Aires, Argentina
Australian Research Council, Centre of Excellence for Mathematics and Statistics of Complex Systems, The University of New South Wales, Sydney, NSW 2052, Australia
School of Mathematics, The University of New South Wales, Sydney, NSW 2052, Australia
Palabras clave:Boundary value problem; Existence of solutions; Time scales; Topological methods
Año:2005
Volumen:308
Número:2
Página de inicio:565
Página de fin:577
DOI: http://dx.doi.org/10.1016/j.jmaa.2004.11.039
Título revista:Journal of Mathematical Analysis and Applications
Título revista abreviado:J. Math. Anal. Appl.
ISSN:0022247X
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v308_n2_p565_Amster

Referencias:

  • Agarwal, R.P., O'Regan, D., Nonlinear boundary value problems on time scales (2001) Nonlinear Anal., 44, pp. 527-535
  • Akin, E., Boundary value problems for a differential equation on a measure chain (2000) Panamer. Math. J., 10, pp. 17-30
  • Amster, P., Mariani, M.C., A fixed point operator for a nonlinear boundary value problem (2002) J. Math. Anal. Appl., 266, pp. 160-168
  • Bobisud, L.E., O'Regan, D., Existence of positive solutions for singular ordinary differential equations with nonlinear boundary conditions (1996) Proc. Amer. Math. Soc., 124, pp. 2081-2087
  • Bohner, M., Peterson, A., (2001) Dynamic Equations on Time Scales. An Introduction With Applications, , Cambridge, MA: Birkhäuser Boston
  • Bohner, M., Guseinov, G., Peterson, A., Introduction to the time scales calculus (2003) Advances in Dynamic Equations on Time Scales, pp. 1-15. , Birkhäuser Boston Cambridge, MA
  • Erbe, L., Peterson, A., Green's functions and comparison theorems for differential equations on measure chains (1999) Dynam. Contin. Discrete Impuls. Systems, 6, pp. 121-137
  • Henderson, J., Peterson, A., Tisdell, C.C., On the existence and uniqueness of solutions to boundary value problems on time scales (2004) Adv. Difference Equations, 2004, pp. 93-109
  • Henderson, J., Tisdell, C.C., Topological transversality and boundary value problems on time scales (2004) J. Math. Anal. Appl., 289, pp. 110-125
  • Hilger, S., Analysis on measure chains - A unified approach to continuous and discrete calculus (1990) Results Math., 18, pp. 18-56
  • Lloyd, N.G., (1978) Degree Theory, 73. , Cambridge Tracts in Math. Cambridge: Cambridge Univ. Press
  • Peterson, A.C., Raffoul, Y.N., Tisdell, C.C., Three point boundary value problems on time scales (2004) J. Differ. Equations Appl., 10, pp. 843-849
  • Thompson, H.B., Systems of differential equations with fully nonlinear boundary conditions (1997) Bull. Austral. Math. Soc., 56, pp. 197-208
  • Tisdell, C.C., Thompson, H.B., On the existence of solutions to boundary value problems on time scales Discrete Contin. Dynam. Systems, , in press

Citas:

---------- APA ----------
Amster, P., Rogers, C. & Tisdell, C.C. (2005) . Existence of solutions to boundary value problems for dynamic systems on time scales. Journal of Mathematical Analysis and Applications, 308(2), 565-577.
http://dx.doi.org/10.1016/j.jmaa.2004.11.039
---------- CHICAGO ----------
Amster, P., Rogers, C., Tisdell, C.C. "Existence of solutions to boundary value problems for dynamic systems on time scales" . Journal of Mathematical Analysis and Applications 308, no. 2 (2005) : 565-577.
http://dx.doi.org/10.1016/j.jmaa.2004.11.039
---------- MLA ----------
Amster, P., Rogers, C., Tisdell, C.C. "Existence of solutions to boundary value problems for dynamic systems on time scales" . Journal of Mathematical Analysis and Applications, vol. 308, no. 2, 2005, pp. 565-577.
http://dx.doi.org/10.1016/j.jmaa.2004.11.039
---------- VANCOUVER ----------
Amster, P., Rogers, C., Tisdell, C.C. Existence of solutions to boundary value problems for dynamic systems on time scales. J. Math. Anal. Appl. 2005;308(2):565-577.
http://dx.doi.org/10.1016/j.jmaa.2004.11.039