About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 708734, 7 pages
http://dx.doi.org/10.1155/2013/708734
Research Article

Existence Results for Solutions of Integral Boundary Value Problems on Time Scales

Department of Mathematics, Ege University, Bornova, 35100 Izmir, Turkey

Received 27 November 2012; Accepted 12 March 2013

Academic Editor: Xinan Hao

Copyright © 2013 Erbil Cetin and F. Serap Topal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. Hilger, “Analysis on measure chains—a unified approach to continuous and discrete calculus,” Results in Mathematics, vol. 18, no. 1-2, pp. 18–56, 1990. View at Zentralblatt MATH · View at MathSciNet
  2. M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston, Mass, USA, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  3. M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, Mass, USA, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  4. F. A. Davidson and B. P. Rynne, “The formulation of second-order boundary value problems on time scales,” Advances in Difference Equations, vol. 2006, Article ID 31430, 10 pages, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. L. Erbe and A. Peterson, “Green's functions and comparison theorems for differential equations on measure chains,” Dynamics of Continuous, Discrete and Impulsive Systems, vol. 6, no. 1, pp. 121–137, 1999. View at Zentralblatt MATH · View at MathSciNet
  6. R. A. Khan, “The generalized method of quasilinearization and nonlinear boundary value problems with integral boundary conditions,” Electronic Journal of Qualitative Theory of Differential Equations, vol. 10, pp. 1–9, 2003. View at Zentralblatt MATH · View at MathSciNet
  7. Z. Yang, “Existence and nonexistence results for positive solutions of an integral boundary value problem,” Nonlinear Analysis: Theory, Methods & Applications, vol. 65, no. 8, pp. 1489–1511, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. B. Ahmad, A. Alsaedi, and B. S. Alghamdi, “Analytic approximation of solutions of the forced Duffing equation with integral boundary conditions,” Nonlinear Analysis: Real World Applications, vol. 9, no. 4, pp. 1727–1740, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. F. M. Atici and G. Sh. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. G. W. Batten Jr., “Second-order correct boundary conditions for the numerical solution of the mixed boundary problem for parabolic equations,” Mathematics of Computation, vol. 17, pp. 405–413, 1963. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J. R. Cannon, S. P. Esteva, and J. van der Hoek, “A Galerkin procedure for the diffusion equation subject to the specification of mass,” SIAM Journal on Numerical Analysis, vol. 24, no. 3, pp. 499–515, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. L. I. Kamynin, “A boundary value problem in the theory of heat conduction with boundary condition,” USSR Computational Mathematics and Mathematical Physics, vol. 4, no. 6, pp. 33–59, 1964. View at Publisher · View at Google Scholar
  13. A. Bouziani and N.-E. Benouar, “Mixed problem with integral conditions for a third order parabolic equation,” Kobe Journal of Mathematics, vol. 15, no. 1, pp. 47–58, 1998. View at Zentralblatt MATH · View at MathSciNet
  14. M. Denche and A. L. Marhoune, “Mixed problem with integral boundary condition for a high order mixed type partial differential equation,” Journal of Applied Mathematics and Stochastic Analysis, vol. 16, no. 1, pp. 69–79, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. J. M. Gallardo, “Second-order differential operators with integral boundary conditions and generation of analytic semigroups,” The Rocky Mountain Journal of Mathematics, vol. 30, no. 4, pp. 1265–1292, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. T. Jankowski, “Differential equations with integral boundary conditions,” Journal of Computational and Applied Mathematics, vol. 147, no. 1, pp. 1–8, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. A. V. Kartynnik, “A three-point mixed problem with an integral condition with respect to the space variable for second-order parabolic equations,” Differential Equations, vol. 26, no. 9, pp. 1160–1166, 1990. View at MathSciNet
  18. L. Liu, X. Hao, and Y. Wu, “Positive solutions for singular second order differential equations with integral boundary conditions,” Mathematical and Computer Modelling, vol. 57, no. 3-4, pp. 836–847, 2013. View at Publisher · View at Google Scholar
  19. X. Zhang and W. Ge, “Symmetric positive solutions of boundary value problems with integral boundary conditions,” Applied Mathematics and Computation, vol. 219, no. 8, pp. 3553–3564, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  20. S. A. Brykalov, “A second-order nonlinear problem with two-point and integral boundary conditions,” Georgian Mathematical Journal, vol. 1, no. 3, pp. 243–249, 1994. View at Zentralblatt MATH · View at MathSciNet
  21. M. A. Krasnosel'skii, Positive Solutions of Operator Equations, P. Noordhoff Ltd., Groningen, The Netherlands, 1964. View at MathSciNet