Rocky Mountain Journal of Mathematics

A Quasilinearization Approach for Two Point Nonlinear Boundary Value Problems on Time Scales

Elvan Akin-Bohner and Ferhan Merdivenci Atici

Full-text: Open access

Article information

Source
Rocky Mountain J. Math., Volume 35, Number 1 (2005), 19-45.

Dates
First available in Project Euclid: 5 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1181069766

Digital Object Identifier
doi:10.1216/rmjm/1181069766

Mathematical Reviews number (MathSciNet)
MR2116472

Zentralblatt MATH identifier
1089.34015

Subjects
Primary: 34B15: Nonlinear boundary value problems
Secondary: 39A12: Discrete version of topics in analysis

Keywords
Measure chains time scales lower and upper solutions boundary value problems convergence quasilinearization

Citation

Akin-Bohner, Elvan; Atici, Ferhan Merdivenci. A Quasilinearization Approach for Two Point Nonlinear Boundary Value Problems on Time Scales. Rocky Mountain J. Math. 35 (2005), no. 1, 19--45. doi:10.1216/rmjm/1181069766. https://projecteuclid.org/euclid.rmjm/1181069766


Export citation

References

  • R.P. Agarwal and M. Bohner, Basic calculus on time scales and some of its applications, Results Math. 35 (1999), 3-22.
  • R.P Agarwal, M. Bohner and D. O'Regan, Time scale boundary value problems on infinite intervals, spec. issue on Dynamic Equations on Time Scales (R.P. Agarwal, M. Bohner and D. O'Regan, eds.), J. Comput. Appl. Math. 141 (2002), 27-34;
  • E. Ak\in, Boundary value problems for a differential equation on a measure chain, Panamer. Math. J. 10 (2000), 17-30.
  • E. Ak\in-Bohner and M. Bohner, The exponential function and Laplace transform for alpha derivatives, Proc. of the Sixth Internat. Conf. on Difference Equations (Augsburg) (B. Aulbach, S. Elaydi and G. Ladas, eds.), Gordon and Breach, to appear.
  • F. Merdivenci At\ic\i, P.W. Eloe and B. Kaymakçalan, The quasilinearization method for boundary value problems on time scales, J. Math. Anal. Appl. 276 (2002), 357-372.
  • F. Merdivenci At\ic\i and G.Sh. Guseinov, On Green's functions and positive solutions for boundary value problems on time scales, J. Comput. Appl. Math. 141 (2002), 75-99.
  • M. Bohner and A. Peterson, Dynamic equations on time scales, Birkhäuser, Boston, 2001.
  • A. Cabada and J.J. Nieto, Quasilinearization and rate of convergence for higher-order nonlinear periodic boundary value problems, J. Optim. Theory Appl. 108 (2001), 97-107.
  • P.W. Eloe, The method of quasilinearization and dynamic equations on compact measure chains, J. Comput. Appl. Math. 141 (2002), 159-167.
  • L. 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.
  • S. Hilger, Ein Maß kettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten, Ph.D. thesis, Universität Würzburg, 1988.
  • B. Kaymakçalan, V. Lakshmikantham and S. Sivasundaram, Dynamic systems on measure chains, Math. Appl., vol. 370, Kluwer Academic Publishers, Dordrecht, 1996.
  • V. Lakshmikantham and A.S. Vatsala, Generalized quasilinearization for nonlinear problems, Kluwer Academic Publishers, Dordrecht, 1998.
  • R.N. Mohapatra, K. Vajravelu and Y. Yin, Generalized quasilinearization method for second order boundary value problems, Nonlinear Anal. 36 (1999), 799-806.