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Abstract and Applied Analysis
Volume 2014, Article ID 526549, 6 pages
http://dx.doi.org/10.1155/2014/526549
Research Article

A Singular Initial-Value Problem for Second-Order Differential Equations

Mathematics and Computing Department, Beykent University, Ayazağa, Şişli, 34396 Istanbul, Turkey

Received 4 December 2013; Accepted 10 March 2014; Published 9 April 2014

Academic Editor: Elena Braverman

Copyright © 2014 Afgan Aslanov. 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. M. Beech, “An approximate solution for the polytrope n=3,” Astrophysics and Space Science, vol. 132, no. 2, pp. 393–396, 1987. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. S. Chandrasekhar, Introduction To the Study of Stellar Structure, Dover, New York, NY, USA, 1967. View at MathSciNet
  3. E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, Tata McGraw-Hill, Bombay, India, 1955. View at MathSciNet
  4. G. P. Horedt, “Exact solutions of the Lane-Emden equation in N-dimensional space,” Astronomy and Astrophysics, vol. 172, no. 1, pp. 359–367, 1987. View at Google Scholar
  5. S. Liao, “A new analytic algorithm of Lane-Emden type equations,” Applied Mathematics and Computation, vol. 142, no. 1, pp. 1–16, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  6. F. K. Liu, “Polytropic gas spheres: an approximate analytic solution of the Lane-Emden equation,” Monthly Notices of the Royal Astronomical Society, vol. 281, pp. 1197–1205, 1996. View at Publisher · View at Google Scholar
  7. Z. F. Seidov and R. K. Kyzakhmetov, “Solutions of the Lane-Emden problem in series,” Soviet Astronomy, vol. 21, pp. 399–400, 1977. View at Google Scholar
  8. N. T. Shawagfeh, “Nonperturbative approximate solution for Lane-Emden equation,” Journal of Mathematical Physics, vol. 34, no. 9, pp. 4364–4369, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  9. H. T. Davis, Introduction to Nonlinear Differential and Integral Equations, Dover, New York, NY, USA, 1962. View at MathSciNet
  10. P. Rosenau, “A note on integration of the Emden-Fowler equation,” International Journal of Non-Linear Mechanics, vol. 19, no. 4, pp. 303–308, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. R. Bellman, Stability Theory of Differential Equations, McGraw-Hill, New York, NY, USA, 1953. View at MathSciNet
  12. P. Habets and F. Zanolin, “Upper and lower solutions for a generalized Emden-Fowler equation,” Journal of Mathematical Analysis and Applications, vol. 181, no. 3, pp. 684–700, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  13. D. Hinton, “An oscillation criterion for solutions of ry2+qyγ=0,” The Michigan Mathematical Journal, vol. 16, pp. 349–352, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. J. Janus and J. Myjak, “A generalized Emden-Fowler equation with a negative exponent,” Nonlinear Analysis. Theory, Methods & Applications, vol. 23, no. 8, pp. 953–970, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. P. G. L. Leach, “First integrals for the modified Emden equation q+αtq+qn=0,” Journal of Mathematical Physics, vol. 26, no. 10, pp. 2510–2514, 1985. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. W. Mydlarczyk, “A singular initial value problem for second and third order differential equations,” Colloquium Mathematicum, vol. 68, no. 2, pp. 249–257, 1995. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. O. U. Richardson, The Emission of Electricity From Hot Bodies, Longman’s Green and Company, London, UK, 1921.
  18. A.-M. Wazwaz, “A new algorithm for solving differential equations of Lane-Emden type,” Applied Mathematics and Computation, vol. 118, no. 2-3, pp. 287–310, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  19. D. C. Biles, M. P. Robinson, and J. S. Spraker, “A generalization of the Lane-Emden equation,” Journal of Mathematical Analysis and Applications, vol. 273, no. 2, pp. 654–666, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  20. R. P. Agarwal and D. O’Regan, “Second order initial value problems of Lane-Emden type,” Applied Mathematics Letters, vol. 20, no. 12, pp. 1198–1205, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  21. R. K. Miller and A. N. Michel, Ordinary Differential Equations, Academic Press, New York, NY, USA, 1982. View at MathSciNet
  22. A. Aslanov, “A generalization of the Lane-Emden equation,” International Journal of Computer Mathematics, vol. 85, no. 11, pp. 1709–1725, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  23. I. T. Kiguradze and A. G. Lomtatidze, “On certain boundary value problems for second-order linear ordinary differential equations with singularities,” Journal of Mathematical Analysis and Applications, vol. 101, no. 2, pp. 325–347, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  24. A. Lomtatidze, “On a nonlocal boundary value problem for second order linear ordinary differential equations,” Journal of Mathematical Analysis and Applications, vol. 193, no. 3, pp. 889–908, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  25. A. Lomtatidze and L. Malaguti, “On a two-point boundary value problem for the second order ordinary differential equations with singularities,” Nonlinear Analysis, Theory, Methods and Applications, vol. 52, no. 6, pp. 1553–1567, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  26. R. P. Agarwal and I. Kiguradze, “On multi-point boundary value problems for linear ordinary differential equations with singularities,” Journal of Mathematical Analysis and Applications, vol. 297, no. 1, pp. 131–151, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus