Skip to main content
SpringerLink
Log in
Book cover

Constant-Sign Solutions of Systems of Integral Equations pp 105–145Cite as

System of Fredholm Integral Equations: Triple Constant-Sign Solutions

  • Chapter
  • First Online:

  • 708 Accesses

Abstract

In this chapter we shall consider two systems of Fredholm integral equations, one is on a finite interval

$$\displaystyle{ u_{i}(t) =\int _{ 0}^{1}g_{ i}(t,s)P_{i}(s,u_{1}(s),u_{2}(s),\cdots \,,u_{n}(s))ds,\ \ t \in [0,1],\ 1 \leq i \leq n }$$
(4.1.1)

and the other is on the half-line [0,∞)

$$\displaystyle{ u_{i}(t) =\int _{ 0}^{\infty }g_{ i}(t,s)P_{i}(s,u_{1}(s),u_{2}(s),\cdots \,,u_{n}(s))ds,\ \ t \in [0,\infty ),\ 1 \leq i \leq n. }$$
(4.1.2)

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. R.P. Agarwal, M. Meehan, D. O’Regan, Nonlinear Integral Equations and Inclusions (Nova Science Publishers, Hungtington, 2001)

    Google Scholar 

  2. R.P. Agarwal, D. O’Regan, Existence of three solutions to integral and discrete equations via the Leggett Williams fixed point theorem. Rocky Mt. J. Math. 31, 23–35 (2001)

    Article  MATH  Google Scholar 

  3. R.P. Agarwal, D. O’Regan, P.J.Y. Wong, Positive Solutions of Differential, Difference and Integral Equations (Kluwer, Dordrecht, 1999)

    Book  MATH  Google Scholar 

  4. R.P. Agarwal, D. O’Regan, P.J.Y. Wong, Constant-sign solutions of a system of Fredholm integral equations. Acta Appl. Math. 80, 57–94 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  5. R.P. Agarwal, D. O’Regan, P.J.Y. Wong, Eigenvalues of a system of Fredholm integral equations. Math. Comput. Model. 39, 1113–1150 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. R.P. Agarwal, D. O’Regan, P.J.Y. Wong, Triple solutions of constant sign for a system of Fredholm integral equations. Cubo 6, 1–45 (2004)

    MathSciNet  MATH  Google Scholar 

  7. R.P. Agarwal, P.J.Y. Wong, Advanced Topics in Difference Equations (Kluwer, Dordrecht, 1997)

    Book  MATH  Google Scholar 

  8. D. Anderson, R.I. Avery, Multiple positive solutions to a third order discrete focal boundary value problem. Comput. Math. Appl. 42, 333–340 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. D. Anderson, R.I. Avery, A.C. Peterson, Three positive solutions to a discrete focal boundary value problem. J. Comput. Appl. Math. 88, 102–118 (1998)

    Article  MathSciNet  Google Scholar 

  10. R.I. Avery, Multiple positive solutions of an nth order focal boundary value problem. Panam. Math. J. 8, 39–55 (1998)

    MathSciNet  MATH  Google Scholar 

  11. R.I. Avery, Existence of multiple positive solutions to a conjugate boundary value problem. Math. Sci. Res. Hot-Line 2, 1–6 (1998)

    MathSciNet  MATH  Google Scholar 

  12. R.I. Avery, A.C. Peterson, Multiple positive solutions of a discrete second order conjugate problem. Panam. Math. J. 8, 1–12 (1998)

    MathSciNet  MATH  Google Scholar 

  13. J.M. Davis, P.W. Eloe, J. Henderson, Triple positive solutions and dependence on higher order derivatives. J. Math. Anal. Appl. 237, 710–720 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  14. L.H. Erbe, S. Hu, H. Wang, Multiple positive solutions of some boundary value problems. J. Math. Anal. Appl. 184, 640–648 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  15. L.H. Erbe, H. Wang, On the existence of positive solutions of ordinary differential equations. Proc. Am. Math. Soc. 120, 743–748 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  16. D. Jiang, On the existence of positive solutions to second order periodic boundary value problems. Acta Math. Sci. 18, 31–35 (1998)

    Google Scholar 

  17. D. Jiang, H. Liu, Existence of positive solutions to second order Neumann boundary value problems. J. Math. Res. Expo. 20, 360–364 (2000)

    MathSciNet  MATH  Google Scholar 

  18. W. Lian, F. Wong, C. Yeh, On the existence of positive solutions of nonlinear second order differential equations. Proc. Am. Math. Soc. 124, 1117–1126 (1996)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

  21. P.J.Y. Wong, Triple positive solutions of conjugate boundary value problems. Comput. Math. Appl. 36, 19–35 (1998)

    Article  MATH  Google Scholar 

  22. P.J.Y. Wong, Solutions of constant signs of a system of Sturm–Liouville boundary value problems. Math. Comput. Model. 29, 27–38 (1999)

    Article  MATH  Google Scholar 

  23. P.J.Y. Wong, Triple positive solutions of conjugate boundary value problems II. Comput. Math. Appl. 40, 537–557 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  24. P.J.Y. Wong, Sharp inequalities for solutions of multipoint boundary value problems. Math. Inequal. Appl. 3, 79–88 (2000)

    MathSciNet  MATH  Google Scholar 

  25. P.J.Y. Wong, Three fixed-sign solutions of system model with Sturm–Liouville type conditions. J. Math. Anal. Appl. 298, 120–145 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  26. P.J.Y. Wong, Triple fixed-sign solutions for a system of third-order generalized right focal boundary value problems, in Proceedings of the Conference on Differential & Difference Equations and Applications, USA (2006), pp. 1139–1148

    Google Scholar 

  27. P.J.Y. Wong, Multiple fixed-sign solutions for a system of generalized right focal problems with deviating arguments. J. Math. Anal. Appl. 323, 100–118 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  28. P.J.Y. Wong, Multiple fixed-sign solutions for a system of higher order three-point boundary value problems with deviating arguments. Comput. Math. Appl. 55, 516–534 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  29. P.J.Y. Wong, R.P. Agarwal, Extension of continuous and discrete inequalities due to Eloe and Henderson. Nonlinear Anal. 34, 479–487 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  30. P.J.Y. Wong, R.P. Agarwal, Multiple positive solutions of two-point right focal boundary value problems. Math. Comput. Model. 28, 41–49 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  31. P.J.Y. Wong, R.P. Agarwal, Multiple solutions of generalized multipoint conjugate boundary value problems. Georgian Math. J. 6, 567–590 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  32. P.J.Y. Wong, R.P. Agarwal, Results and estimates on multiple solutions of Lidstone boundary value problems. Acta Math. Hung. 86, 137–168 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  33. P.J.Y. Wong, Y.C. Soh, Triple fixed-sign solutions in modelling a system with Hermite boundary conditions. J. Inequal. Appl. 4, 363–385 (2005)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Texas A&M University – Kingsville, Kingsville, TX, USA

    Ravi P. Agarwal

  2. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Galway, Ireland

    Donal O’Regan

  3. School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore, Singapore

    Patricia J. Y. Wong

Authors
  1. Ravi P. Agarwal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Donal O’Regan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Patricia J. Y. Wong
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Agarwal, R.P., O’Regan, D., Wong, P.J.Y. (2013). System of Fredholm Integral Equations: Triple Constant-Sign Solutions. In: Constant-Sign Solutions of Systems of Integral Equations. Springer, Cham. https://doi.org/10.1007/978-3-319-01255-1_4

Download citation

Publish with us

Policies and ethics

Search

Navigation