, Volume 12, Issue 4, pp 725–732 | Cite as

Existence and uniqueness of solutions for singular integral equation

  • Zhongwei Cao
  • Daqing Jiang
  • Chengjun Yuan
  • Donal O’Regan


Using the mixed monotone method we establish existence and uniqueness results for a singular integral equation. The theorem obtained is very general and complements previous known results.


Mixed monotone operator integral equation singular existence uniqueness 

Mathematics Subject Classification (2000)

34B15 34B16 


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  1. 1.
    R.P. Agarwal, D. O’Regan, A note on a singular integral equation arising in a problem in communications, Z. Angew. Math. Mech., 81 (2001), 499–504.Google Scholar
  2. 2.
    R.P. Agarwal, D. O’Regan, Multiplicity results for singular conjugate, focal and (n, p) problems, J. Differ. Equ. 170 (2001), 142–156.Google Scholar
  3. 3.
    R.P. Agarwal, D. O’Regan, Singular Differential and Integral Equations with Applications, Kluwer Academic. Publication Dordrecht, 2003.Google Scholar
  4. 4.
    R.P. Agarwal, D.O’Regan, Positive solutions for (p, np) conjugate boundary value problems, J. Differ. Equ. 150 (1998), 462–473.Google Scholar
  5. 5.
    P.W. Eloe, J. Henderson, Singular non–linear (k, nk) conjugate boundary value problems, J. Differ. Equ. 133 (1997), 136–151.Google Scholar
  6. 6.
    D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press. Inc., New York, (1988)Google Scholar
  7. 7.
    D.Q. Jiang, Multiple Positive Solutions to singular boundary value problems for superlinear higher order ODEs, Comput. Math. Appl. 40 (2000), 249–259.Google Scholar
  8. 8.
    S. Karlin, L. Nirenberg, On a theorem of P. Nowosad, J. Math. Anal. Appl., 17 (1967), 61–67.Google Scholar
  9. 9.
    D. O’Regan, M. Meehan, Existence Theory for Nonlinear Integral and Integrodifferential Equations, Kluwer Academic Publication, Dordrecht, (1998)Google Scholar
  10. 10.
    D. Guo, The Order Methods in Nonlinear Analysis, Shandong Technical and Science Press, Jinan (2000, in Chinese).Google Scholar
  11. 11.
    Xiaoning Lin, Daqing Jiang and Xiaoyue Li, Existence and uniqueness of solutions for singular (k, n – k) conjugate boundary value problems, Comput. Math. Appl. 52 (2006), 375–382.Google Scholar
  12. 12.
    X. N. Lin, X. Y. Li and D. Q. Jiang, Existence and uniqueness of solutions for singular fourth-order boundary value problems, J. Comput. Appl. Math. 196 (2006), 155–161.Google Scholar

Copyright information

© Springer Science + Business Media B.V. 2008

Authors and Affiliations

  • Zhongwei Cao
    • 1
  • Daqing Jiang
    • 2
  • Chengjun Yuan
    • 3
  • Donal O’Regan
    • 4
  1. 1.Department of Applied MathematicsChangchun Taxation CollegeChangchunP.R.China
  2. 2.School of Mathematics and StatisticsNortheast Normal UniversityChangchunP.R.China
  3. 3.School of Mathematics and ComputerHarbin UniversityHarbinP.R.China
  4. 4.Department of MathematicsNational University of IrelandGalwayIreland

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