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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 957696, 7 pages
http://dx.doi.org/10.1155/2013/957696
Research Article

Asymptotic Behavior of Solutions to a Vector Integral Equation with Deviating Arguments

Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, Spain

Received 31 July 2013; Accepted 5 November 2013

Academic Editor: István Györi

Copyright © 2013 Cristóbal González and Antonio Jiménez-Melado. 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. F. V. Atkinson, “On second order nonlinear oscillation,” Pacific Journal of Mathematics, vol. 5, pp. 643–647, 1955. View at Google Scholar
  2. A. Constantin, “On the existence of positive solutions of second order differential equations,” Annali di Matematica Pura ed Applicata. Series IV, vol. 184, no. 2, pp. 131–138, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. S. G. Dubé and A. B. Mingarelli, “Note on a non-oscillation theorem of Atkinson,” Electronic Journal of Differential Equations, vol. 2004, article 22, 6 pages, 2004, http://ejde.math.txstate.edu. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. M. Ehrnström, “Positive solutions for second-order nonlinear differential equations,” Nonlinear Analysis: Theory, Methods & Applications A, vol. 64, no. 7, pp. 1608–1620, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. M. Ehrnström, “Linear asymptotic behaviour of second order ordinary differential equations,” Glasgow Mathematical Journal, vol. 49, no. 1, pp. 105–120, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. C. González and A. Jiménez-Melado, “Existence of monotonic asymptotically constant solutions for second order differential equations,” Glasgow Mathematical Journal, vol. 49, no. 3, pp. 515–523, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. C. González and A. Jiménez-Melado, “Asymptotic behavior of solutions to an integral equation underlying a second-order differential equation,” Nonlinear Analysis: Theory, Methods & Applications A, vol. 70, no. 2, pp. 822–829, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. O. Lipovan, “On the asymptotic behaviour of the solutions to a class of second order nonlinear differential equations,” Glasgow Mathematical Journal, vol. 45, no. 1, pp. 179–187, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. O. G. Mustafa and Y. V. Rogovchenko, “Global existence of solutions with prescribed asymptotic behavior for second-order nonlinear differential equations,” Nonlinear Analysis: Theory, Methods & Applications A, vol. 51, no. 2, pp. 339–368, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. E. Wahlén, “Positive solutions of second-order differential equations,” Nonlinear Analysis: Theory, Methods & Applications A, vol. 58, no. 3-4, pp. 359–366, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. G. E. Ladas and V. Lakshmikantham, Differential Equations in Abstract Spaces, vol. 85 of Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1972. View at MathSciNet
  12. E. Zeidler, Nonlinear Functional Analysis and Its Applications. I, Fixed-Point Theorems, Springer, New York, NY, USA, 1986, Translated from the German by P. R. Wadsack. View at Publisher · View at Google Scholar · View at MathSciNet
  13. J. Dugundji, Topology, Allyn and Bacon, Boston, Mass, USA, 1966. View at MathSciNet
  14. S. Mazur, “Uber die kleinste konvexe Menge, die eine gegebene kompakte Menge enthalt,” Studia Mathematica, vol. 2, pp. 7–9, 1930. View at Google Scholar