Journal of Integral Equations and Applications

Solvability of a quadratic Hammerstein integral equation in the class of functions having limits at infinity

Ravi P. Agarwal, Józef Banaś, Kamil Banaś, and Donal O'Regan

Full-text: Open access

Article information

J. Integral Equations Applications, Volume 23, Number 2 (2011), 157-181.

First available in Project Euclid: 20 June 2011

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Quadratic Hammerstein integral equation superposition operator measure of noncompactness fixed point theorem of Darbo type


Agarwal, Ravi P.; Banaś, Józef; Banaś, Kamil; O'Regan, Donal. Solvability of a quadratic Hammerstein integral equation in the class of functions having limits at infinity. J. Integral Equations Applications 23 (2011), no. 2, 157--181. doi:10.1216/JIE-2011-23-2-157.

Export citation


  • R.P. Agarwal, D. O'Regan and P.J.Y. Wong, Positive solutions of differential, difference and integral equation, Kluwer Academic Publishers, Dordrecht, 1999.
  • R.R. Akmerov, M.I. Kamenskii, A.S. Potapov, A.E. Rodkina and B.N. Sadovskii, Measures of noncompactness and condensing operators, Birkhäuser Verlag, Basel, 1992.
  • J. Appell and P.P. Zabrejko, Nonlinear superposition operators, Cambridge University Press, Cambridge, 1990.
  • J.M. Ayerbe Toledano, T. Dominguez Benavides and G. Lopez Acedo, Measures of noncompactness in metric fixed point theory, Birkhäuser, Basel, 1997.
  • J. Banaś, Measures of noncompactness in the space of continuous tempered functions, Demon. Math. 14 (1981), 127-133.
  • J. Banaś and K. Goebel, Measures of noncompactness in Banach spaces, Lect. Notes Pure Appl. Math. 60 (1980), Dekker, New York.
  • J. Banaś, D. O'Regan and R.P. Agarwal, Measures of noncompactness and asymptotic stablility of solutions of a quadratic Hammerstein integral equation, Rocky Mountain J. Math., to appear.
  • J. Banaś, D. O'Regan and K. Sadarangani, On solutions of a quadratic Hammerstein integral equation on an unbounded interval, Dynamic Syst. Appl. 18 (2009), 251-264.
  • J. Banaś, J. Rocha Martin and K. Sadarangani, On solutions of a quadratic integral equation of Hammerstein type, Math. Comput. Model. 43 (2006), 97-104.
  • C. Corduneanu, Integral equations and applications, Cambridge University Press, Cambridge, 1991.
  • G. Darbo, Punti uniti in transformazioni a codominio non compatto, Rend. Sem. Math. Univ. Padova 24 (1955), 84-92.
  • K. Deimling, Nonlinear functional analysis, Springer Verlag, Berlin, 1985.
  • G.M. Fichtenholz, Differential and integral calculus, II, PWN, Warsaw, 1980 (in Polish).
  • J. Mawhin, On an existence result of Leray for nonlinear integral equations, Fixed Point Theory 7 (2006), 297-304.
  • D. O'Regan and M. Meehan, Existence theory for nonlinear integral and integrodifferential equations, Kluwer Academic Publishers, Dordrecht, 1998.
  • R. Stańczy, Hammerstein equations with an integral over a noncompact domain, Ann. Polon. Math. 69 (1998), 49-60.
  • Z. Yang, Nontrivial solutions of nonlinear Hammerstein integral equations, Nonlin. Funct. Anal. Appl. 10 (2005), 331-342.
  • P.P. Zabrejko, A.I. Koshelev, M.A. Krasnoselśkii, S.G. Mikhlin, L.S. Rakovschik and J. Stetsenko, Integral equations, Nordhoff, Leyden, 1975.