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System of Volterra Integral Equations: Constant-Sign Solutions in Orlicz Spaces

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Constant-Sign Solutions of Systems of Integral Equations

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Abstract

In this chapter we shall consider the system of Volterra integral equations

$$\displaystyle{ u_{i}(t) =\int _{ 0}^{t}g_{ i}(t,s)f_{i}(s,u_{1}(s),u_{2}(s),\cdots \,,u_{n}(s))ds,\ \ a.e.\ t \in [0,T],\ 1 \leq i \leq n. }$$
(17.1.1)

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References

  1. 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 

  2. 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 

  3. R.P. Agarwal, D. O’Regan, P.J.Y. Wong, Constant-sign L p solutions for a system of integral equations. Results Math. 46, 195–219 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  4. R.P. Agarwal, D. O’Regan, P.J.Y. Wong, Constant-sign solutions of a system of Volterra integral equations. Comput. Math. Appl. 54, 58–75 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. R.P. Agarwal, D. O’Regan, P.J.Y. Wong, Constant-sign solutions of a system of Volterra integral equations in Orlicz spaces. J. Integr. Equat. Appl. 20, 337–378 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. R.P. Agarwal, D. O’Regan, P.J.Y. Wong, Solutions of a system of integral equations in Orlicz spaces. J. Integr. Equat. Appl. 21, 469–498 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. P.J. Bushell, W. Okrasiński, Uniqueness of solutions for a class of nonlinear Volterra integral equations with convolution kernel. Math. Proc. Camb. Philos. Soc. 106, 547–552 (1989)

    Article  MATH  Google Scholar 

  8. P.J. Bushell, W. Okrasiński, Nonlinear Volterra integral equations with convolution kernel. J. Lond. Math. Soc. 41, 503–510 (1990)

    Article  MATH  Google Scholar 

  9. C. Corduneanu, Integral Equations and Stability of Feedback Systems (Academic, New York, 1973)

    MATH  Google Scholar 

  10. C. Corduneanu, Integral Equations and Applications (Cambridge University Press, New York, 1990)

    Google Scholar 

  11. M.A. Krasnosel’skii, Topological Methods in the Theory of Nonlinear Integral Equations (Pergamon Press, Oxford, 1964)

    Google Scholar 

  12. M.A. Krasnosel’skii, Ya.B. Rutickii, Convex Functions and Orlicz Spaces (Trans. L.F. Boron) (Noordhoff, Groningen, 1961)

    Google Scholar 

  13. M. Meehan, D. O’Regan, Positive solutions of Volterra integral equations using integral inequalities. J. Inequal. Appl. 7, 285–307 (2002)

    MathSciNet  MATH  Google Scholar 

  14. D. O’Regan, Solutions in Orlicz spaces to Uryson integral equations. Proc. R. Ir. Acad. Sect. A 96, 67–78 (1996)

    MATH  Google Scholar 

  15. D. O’Regan, A topological approach to integral inclusions. Proc. R. Ir. Acad. Sect. A 97, 101–111 (1997)

    MATH  Google Scholar 

  16. W. Orlicz, S. Szufla, On the structure of L ϕ-solution sets of integral equations in Banach spaces. Stud. Math. 77, 465–477 (1984)

    MathSciNet  MATH  Google Scholar 

  17. M.M. Rao, Z.D. Ren, Theory of Orlicz Spaces (Dekker, New York, 1991)

    MATH  Google Scholar 

  18. R.L. Wheeden, A. Zygmund, Measure and Integral, Monographs and Textbooks in Pure and Applied Mathematics (Dekker, New York, 1977)

    Google Scholar 

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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
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  2. Donal O’Regan
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  3. Patricia J. Y. Wong
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Agarwal, R.P., O’Regan, D., Wong, P.J.Y. (2013). System of Volterra Integral Equations: Constant-Sign Solutions in Orlicz Spaces. In: Constant-Sign Solutions of Systems of Integral Equations. Springer, Cham. https://doi.org/10.1007/978-3-319-01255-1_17

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