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Existence and uniqueness of solutions for singular integral equation


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.

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  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. 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. R.P. Agarwal, D. O’Regan, Singular Differential and Integral Equations with Applications, Kluwer Academic. Publication Dordrecht, 2003.

  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. P.W. Eloe, J. Henderson, Singular non–linear (k, nk) conjugate boundary value problems, J. Differ. Equ. 133 (1997), 136–151.

    Google Scholar 

  6. D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press. Inc., New York, (1988)

  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. S. Karlin, L. Nirenberg, On a theorem of P. Nowosad, J. Math. Anal. Appl., 17 (1967), 61–67.

  9. D. O’Regan, M. Meehan, Existence Theory for Nonlinear Integral and Integrodifferential Equations, Kluwer Academic Publication, Dordrecht, (1998)

  10. D. Guo, The Order Methods in Nonlinear Analysis, Shandong Technical and Science Press, Jinan (2000, in Chinese).

  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.

  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 

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Correspondence to Zhongwei Cao.

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The work was supported by the National Natural Science Foundation of China (No.10571021 and No.10701020) and Key Laboratory for Applied Statistics of MOE(KLAS) and Subject Foundation of Harbin University (No. HXK200714).

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Cao, Z., Jiang, D., Yuan, C. et al. Existence and uniqueness of solutions for singular integral equation. Positivity 12, 725–732 (2008).

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Mathematics Subject Classification (2000)