Boundary Value Problems
Volume 2009 (2009), Article ID 895290, 2 pages
doi:10.1155/2009/895290
Editorial

Singular Boundary Value Problems for Ordinary Differential Equations

Juan J. Nieto1 and Donal O'Regan2

1Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782 Santiago de Compostela, Spain
2Department of Mathematics, National University of Ireland, Galway, Ireland

Received 31 December 2009; Accepted 31 December 2009

Copyright © 2009 Juan J. Nieto and Donal O'Regan. 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.

Singular boundary value problems for ordinary differential equations model many real world phenomena ranging from different physics equations to biological, physiological, and medical processes [1–3].

This special issue places its emphasis on the study, theory, and applications of boundary value problems involving singularities. It includes some review articles such as [4], equations with discontinuous nonlinearities [5], boundary value problems with uncertainty [6], fractional differential equations [7], periodic or antiperiodic solutions [8], and biological [9] or medical applications [10]. Different methods and techniques are used ranging from variational methods [11] to bifurcation techniques [12].

The editors aimed at a volume that may serve as a reference in the topic of the special issue and collect twenty five original and cutting-edge research articles by some of the top researchers in boundary value problems for ordinary differential equations worldwide and from many different countries (Algeria, Austria, Bulgaria, China, Czech Republic, Greece, Iran, Ireland, Italy, Japan, New Zealand, Pakistan, Saudi Arabia, South Korea, Spain, USA).

We would like to thank the authors for their contributions, the Editor-in-Chief of the journal, Professor Ravi P. Agarwal, and the Editorial Office of the journal for their support.

References

  1. R. P. Agarwal and D. O'Regan, Singular Differential and Integral Equations with Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2003.
  2. A. Cabada, E. Liz, and J. J. Nieto, Mathematical Models in Engineering, Biology and Medicine, American Institute of Physics, Melville, NY, USA, 2009.
  3. D. O'Regan, Theory of Singular Boundary Value Problems, World Scientific Publishing, River Edge, NJ, USA, 1994.
  4. J. Chu and J. J. Nieto, “Recent existence results for second-order singular periodic differential equations,” Boundary Value Problems, vol. 2009, Article ID 540863, 20 pages, 2009.
  5. D. C. Biles and R. López-Pouso, “First-order singular and discontinuous differential equations,” Boundary Value Problems, vol. 2009, Article ID 507671, 25 pages, 2009.
  6. A. Khastan, F. Bahrami, and K. Ivaz, “New results on multiple solutions for Nth-order fuzzy differential equations under generalized differentiability,” Boundary Value Problems, vol. 2009, Article ID 395714, 13 pages, 2009.
  7. M. Belmekki, J. J. Nieto, and R. Rodríguez-López, “Existence of periodic solution for a nonlinear fractional differential equation,” Boundary Value Problems, vol. 2009, Article ID 324561, 18 pages, 2009.
  8. Y. Q. Chen, D. O'Regan, F. L. Wang, and S. L. Zhou, “Antiperiodic boundary value problems for finite dimensional differential systems,” Boundary Value Problems, vol. 2009, Article ID 541435, 11 pages, 2009.
  9. Y. Yu, J. J. Nieto, A. Torres, and K. Wang, “A viral infection model with a nonlinear infection rate,” Boundary Value Problems, vol. 2009, Article ID 958016, 19 pages, 2009.
  10. J. O. Alzabut, J. J. Nieto, and G. Tr. Stamov, “Existence and exponential stability of positive almost periodic solutions for a model of hematopoiesis,” Boundary Value Problems, vol. 2009, Article ID 127510, 10 pages, 2009.
  11. R. P. Agarwal, M. E. Filippakis, D. O'Regan, and N. S. Papageorgiou, “Constant sign and nodal solutions for problems with the p-Laplacian and a nonsmooth potential using variational techniques,” Boundary Value Problems, vol. 2009, Article ID 820237, 32 pages, 2009.
  12. Y. Liu and D. O'Regan, “Multiplicity results using bifurcation techniques for a class of fourth-order m-point boundary value problems,” Boundary Value Problems, vol. 2009, Article ID 970135, 20 pages, 2009.