Abstract and Applied Analysis

Upper and Lower Solution Method for Fourth-Order Four-Point Boundary Value Problem on Time Scales

Ilkay Yaslan Karaca

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We consider a fourth-order four-point boundary value problem for dynamic equations on time scales. By the upper and lower solution method, some results on the existence of solutions of the fourth-order four-point boundary value problem on time scales are obtained. An example is also included to illustrate our results.

Article information

Source
Abstr. Appl. Anal. Volume 2012, Special Issue (2012), Article ID647235, 14 pages.

Dates
First available: 15 February 2012

Permanent link to this document
http://projecteuclid.org/euclid.aaa/1329337694

Digital Object Identifier
doi:10.1155/2012/647235

Mathematical Reviews number (MathSciNet)
MR2872303

Zentralblatt MATH identifier
1229.34139

Citation

Karaca, Ilkay Yaslan. Upper and Lower Solution Method for Fourth-Order Four-Point Boundary Value Problem on Time Scales. Abstract and Applied Analysis 2012, Special Issue (2012), 1--14. doi:10.1155/2012/647235. http://projecteuclid.org/euclid.aaa/1329337694.


Export citation

References

  • M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Application, Birkhäuser Boston, Boston, Mass, USA, 2001.
  • M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhäuser Boston, Boston, Mass, USA, 2003.
  • E. Akin, “Boundary value problems for a differential equation on a measure chain,” Panamerican Mathematical Journal, vol. 10, no. 3, pp. 17–30, 2000.
  • F. M. Atici and A. Cabada, “Existence and uniqueness results for discrete second-order periodic boundary value problems,” Computers & Mathematics with Applications, vol. 45, no. 6-9, pp. 1417–1427, 2003.
  • P. W. Eloe and Q. Sheng, “Approximating crossed symmetric solutions of nonlinear dynamic equations via quasilinearization,” Nonlinear Analysis: Theory, Methods & Applications A, vol. 56, no. 2, pp. 253–272, 2004.
  • B. Kaymakçalan, “Monotone iterative method for dynamic systems on time scales,” Dynamic Systems and Applications, vol. 2, no. 2, pp. 213–220, 1993.
  • S. Leela and S. Sivasundaram, “Dynamic systems on time scales and superlinear convergence of iterative process,” WSSIAA, vol. 3, pp. 431–436, 1994.
  • Y. Pang and Z. Bai, “Upper and lower solution method for a fourth-order four-point boundary value problem on time scales,” Applied Mathematics and Computation, vol. 215, no. 6, pp. 2243–2247, 2009.
  • F. M. Atici and G. S. Guseinov, “On Green's functions and positive solutions for boundary value problems on time scales,” Journal of Computational and Applied Mathematics, vol. 141, no. 1-2, pp. 75–99, 2002.