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International Journal of Differential Equations
Volume 2011 (2011), Article ID 986948, 13 pages
http://dx.doi.org/10.1155/2011/986948
Research Article

Nonlinear Singular BVP of Limit Circle Type and the Presence of Reverse-Ordered Upper and Lower Solutions

1Department of Mathematics, BITS Pilani, Pilani, Rajasthan 333031, India
2Department of Mathematics and Astronomy, University of Lucknow, Lucknow 226007, India

Received 27 May 2011; Accepted 3 July 2011

Academic Editor: Mohamed A. El-Gebeily

Copyright © 2011 Amit K. Verma and Lajja Verma. 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. Y. Zhang, β€œPositive solutions of singular sublinear Dirichlet boundary value problems,” SIAM Journal on Mathematical Analysis, vol. 26, no. 2, pp. 329–339, 1995. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  2. D. O'Regan and M. A. El-Gebeily, β€œExistence, upper and lower solutions and quasilinearization for singular differential equations,” IMA Journal of Applied Mathematics, vol. 73, no. 2, pp. 323–344, 2008. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  3. A. K. Verma, β€œThe monotone iterative method and zeros of Bessel functions for nonlinear singular derivative dependent BVP in the presence of upper and lower solutions,” Nonlinear Analysis, Theory, Methods and Applications, vol. 74, no. 14, pp. 4709–4717, 2011. View at Publisher Β· View at Google Scholar
  4. M. Cherpion, C. de Coster, and P. Habets, β€œA constructive monotone iterative method for second-order BVP in the presence of lower and upper solutions,” Applied Mathematics and Computation, vol. 123, no. 1, pp. 75–91, 2001. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  5. C. de Coster and P. Habets, Two-Point Boundary Value Problems: Lower and Upper Solutions, vol. 205 of Mathematics in Science and Engineering, Elsevier, Amsterdam, The Netherlands, 2006.
  6. D. O'Regan, β€œExistence theory for nonresonant singular boundary value problems,” Proceedings of the Edinburgh Mathematical Society, vol. 38, no. 3, pp. 431–447, 1995. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  7. E. C. Titchmarsh, Eigen Function Expansion. Part I, Oxford University Press, Oxford, UK, 1962.