Journal of Integral Equations and Applications

Solutions of a system of integral equations in Orlicz spaces

Ravi P. Agarwal, Donal O'Regan, and Patricia J.Y. Wong

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J. Integral Equations Applications, Volume 21, Number 4 (2009), 469-498.

First available in Project Euclid: 31 December 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 45G05: Singular nonlinear integral equations 45G15: Systems of nonlinear integral equations 45M20: Positive solutions

System of integral equations Orlicz spaces constantsign solutions


Agarwal, Ravi P.; O'Regan, Donal; Wong, Patricia J.Y. Solutions of a system of integral equations in Orlicz spaces. J. Integral Equations Applications 21 (2009), no. 4, 469--498. doi:10.1216/JIE-2009-21-4-469.

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  • R.P. Agarwal, D. O'Regan and P.J.Y. Wong, Positive Solutions of differential, difference and integral equations, Kluwer, Dordrecht, 1999.
  • --------, Constant-sign solutions of a system of Fredholm integral equations, Acta Appl. Math. 80 (2004), 57-94.
  • --------, Eigenvalues of a system of Fredholm integral equations, Math. Comput. Modelling 39 (2004), 1113-1150.
  • --------, Triple solutions of constant sign for a system of Fredholm integral equations, Cubo 6 (2004), 1-45.
  • --------, Constant-sign $L^p$ solutions for a system of integral equations, Results Mathematics 46 (2004), 195-219.
  • --------, Constant-sign solutions of a system of integral equations: The semipositone and singular case, Asymptotic Anal. 43 (2005), 47-74.
  • --------, Constant-sign periodic and almost periodic solutions for a system of integral equations, Acta Appl. Math. 89 (2005), 177-216.
  • J. Appell, The importance of being Orlicz, Orlicz Centenary Volume, 21-28, Banach Center Publ. 64, Polish Academy Sciences, Warsaw, 2004.
  • J. Appell, E. De Pascale, H.T. Nguyen and P.P. Zabreiko, Nonlinear integral inclusions of Hammerstein type, Topol. Methods Nonlin. Anal. 5 (1995), 111-124.
  • J. Appell and M. Väth, Weakly singular Hammerstein-Volterra operators in Orlicz and Hölder spaces, Z. Anal. Anwend. 12 (1993), 663-676.
  • C. Corduneanu, Integral equations and stability of feedback systems, Academic Press, New York, 1973.
  • --------, Integral equations and applications, Cambridge University Press, New York, 1990.
  • G. Infante and J.R.L. Webb, Nonlinear non-local boundary-value problems and perturbed Hammerstein integral equations, Proc. Edinburgh Math. Soc. 49 (2006), 637-656.
  • M.A. Krasnosel'skii, Positive Solutions of operator equations, Noordhoff, Groningen, 1964.
  • --------, Topological methods in the theory of nonlinear integral equations, Pergamon Press, Oxford, 1964.
  • M.A. Krasnosel'skii and Ya.B. Rutickii, Convex functions and Orlicz spaces, Noordhoff, Groningen, 1961 (trans. L.F. Boron).
  • K.Q. Lan, Positive solutions of semi-positone Hammerstein integral equations and applications, Comm. Pure Appl. Anal. 6 (2007), 441-451.
  • F. Li, Y. Li and Z. Liang, Existence of solutions to nonlinear Hammerstein integral equations and applications, J. Math. Anal. Appl. 323 (2006), 209-227.
  • H. Liang, H. Pang and W. Ge, Triple positive solutions for boundary value problems on infinite intervals, Nonlinear Analysis 67 (2007), 2199-2207.
  • D. O'Regan, Solutions in Orlicz spaces to Uryson integral equations, Proc. Royal Irish Acad. 96 (1996), 67-78.
  • --------, A topological approach to integral inclusions, Proc Royal Irish Acad. 97 (1997), 101-111.
  • W. Orlicz and S. Szufla, On the structure of $L_\phi$-solution sets of integral equations in Banach spaces, Studia Math. 77 (1984), 465-477.
  • R. Pluciennik, The superposition operator in Musielak-Orlicz spaces of vector-valued functions, Rend. Circ. Mat. Palermo %(2) Suppl. No. 14 (1987), 411-417.
  • M.M. Rao and Z.D. Ren, Theory of Orlicz spaces, Marcel Dekker, New York, 1991.