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Nonlinear Boundary Value Problems on Semi-Infinite Intervals using Weighted Spaces: An Upper and Lower Solution Approach

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Abstract

This paper presents a lower and upper solution approach for singular second order boundary value problems on the half line and establishes the existence of positive, unbounded and monotone solutions.

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References

  1. R.P. Agarwal, D. O'Regan, Nonlinear superlinear second order boundary value problems, Journal of Differential Equations, 43 (1998), 60–95.

    Google Scholar 

  2. R.P. Agarwal, D. O'Regan, Second order boundary value problems of singular type, Journal of Mathematical Analysis and Applications, 226 (1998), 414–430.

    Google Scholar 

  3. R.P. Agarwal, D. O'Regan, Infinite interval problems for differential, difference and integral equations, Kluwer Academic Publisher, Dordrecht (2001).

  4. R.P. Agarwal, D. O'Regan, Boundary value problems on the half line modelling phenomena in the theory of colloids, Mathematical Problems in Engineering, 8 (2002), 143–150.

  5. R.P. Agarwal, D. O'Regan, Continuous and discrete boundary value problems on the infinite interval: existence theory, Mathematika, 48 (2001), 273–292.

  6. R.P. Agarwal, D. O'Regan, Infinite interval problems modelling phenomena which arise in the theory of plasma and electrical potential theory, Studies in Appl.Math., 111 (2003), 339–358.

  7. R.P. Agarwal, D. O'Regan, Nonlinear boundary value problems on the semi-infinite interval: An upper and lower solution approach, Mathematika, 49 (2002), 129–140.

  8. R.P. Agarwal, D. O'Regan, Singular problems on the infinite interval modelling phenomena in draining flows, IMA Journal of Applied Mathematics, 66 (2001), 621–635.

    Google Scholar 

  9. J.V. Baxley, Existence and uniqueness for nonlinear boundary value problems on infinite intervals, Journal of Mathematical Analysis and Applications, 147 (1990), 127–133.

    Google Scholar 

  10. L.E. Bobisud, Existence of solutions for nonlinear singular boundary value problems, Applicable Analysis, 35 (1990), 43–57.

    Google Scholar 

  11. L.E. Bosbisud, D. O'Regan, W.D. Royalty, Solvability of some nonlinear boundary value problems, Nonlinear Analysis, 12 (1988), 855–869.

    Google Scholar 

  12. Shaozhu Chen, Yong Zhang, Singular boundary value problems on a half-line, Journal of Mathematical Analysis and Applications, 195 (1995), 449–468.

  13. C. Corduneanu, ``Integral equations and stability of feedback systems'', Academic Press, New York (1973).

  14. Guo Dajun, V. Lakshmikantham, ``Nonlinear problems in abstract cones'', Academic Press, Inc., New York (1988).

  15. Dajun Guo, Boundary value problems for impulsive integro-differential equation on unbounded domains in a Banach Space, Applied Mathematics and Computation, 99 (1999), 1–15.

    Google Scholar 

  16. Patrick Habets, Fabio Zanolin, Upper and lower solutions for a generalized Emden-Fowler equation, Journal of Mathematical Analysis and Applications, 181 (1994), 684–700.

  17. Xiyu Liu, Some existence and nonexistence principles for a class of singular boundary value problems, Nonlinear Analysis, 27(10) (1996), 1147–1164.

    Google Scholar 

  18. M. Meehan, D. O'Regan, Existence theory for nonlinear Fredholm and Volterra integral equations on half-open intervals, Nonlinear Analysis, 35 (1999), 355–387.

    Google Scholar 

  19. M. Meehan, D. O'Regan, Multiple nonnegative solutions of nonlinear integral equations on compact and semi-infinite intervals, Applicable Analysis, 74 (2000), 413–427.

    Google Scholar 

  20. P. Kelevedjiev, Nonnegative solutions to some singular second-order boundary value problems, Nonlinear Analysis, 36 (1999), 481–494.

    Google Scholar 

  21. D. O'Regan, ``Theory of singular boundary value problems'', World Scientific, Singapore (1994).

  22. D. O'Regan, ``Existence theory for ordinary differential equations'', Kluwer, Dordrecht (1997).

  23. P.K. Palamides, G.N. Galanis, Positive, unbounded and monotone solutions of the singular second Painlevé equation on the half-line, Nonlinear Analysis, 57 (2004), 401–419.

    Google Scholar 

  24. P.K. Palamides, Generalized Painleve equation and superconductivity: asymptotic behavior of unbounded solutions, Mathematical and Computer Modelling, 38 (2003), 177–189.

  25. B. Yan, Multiple unbounded solutions of boundary value problems for second order differential equations on the half line, Nonlinear Analysis, 51 (2002), 1031–1044.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, National University of Ireland, Galway, Ireland

    Donal O'Regan

  2. Department of Mathematics, Shandong Normal University, Ji-nan, 250014, P.R.China

    Baoqiang Yan

  3. Department of Mathematical Science, Florida Institute of Technology, Melbourne, Florida, 32901, USA

    Ravi P. Agarwal

Authors
  1. Donal O'Regan
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  2. Baoqiang Yan
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  3. Ravi P. Agarwal
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Additional information

The project is supported by the fund of National Natural Science(10571111) and the fund of Natural Science of Shandong Province(Y2005A07).

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O'Regan, D., Yan, B. & Agarwal, R. Nonlinear Boundary Value Problems on Semi-Infinite Intervals using Weighted Spaces: An Upper and Lower Solution Approach. Positivity 11, 171–189 (2007). https://doi.org/10.1007/s11117-006-0050-5

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  • DOI: https://doi.org/10.1007/s11117-006-0050-5

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