Topological Methods in Nonlinear Analysis

Aronszajn type results for Volterra equations and inclusions

Ravi P. Agarwal, Lech Górniewicz, and Donal O'Regan

Full-text: Open access

Abstract

This paper discusses the topological structure of the set of solutions for a variety of Volterra equations and inclusions. Our results rely on the existence of a maximal solution for an appropriate ordinary differential equation.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 23, Number 1 (2004), 149-159.

Dates
First available in Project Euclid: 31 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1464731382

Mathematical Reviews number (MathSciNet)
MR2055330

Zentralblatt MATH identifier
1064.45010

Citation

Agarwal, Ravi P.; Górniewicz, Lech; O'Regan, Donal. Aronszajn type results for Volterra equations and inclusions. Topol. Methods Nonlinear Anal. 23 (2004), no. 1, 149--159. https://projecteuclid.org/euclid.tmna/1464731382


Export citation

References

  • \ref\key 1 J. P. Aubin and A. Cellina, Differential Inclusions, Springer–Verlag, New York (1984)
  • \ref\key 2 J. Conway, A Course in Functional Analysis, Springer–Verlag, New York(1990)
  • \ref\key 3 C. Corduneanu, Integral Equations and Applications, Cambridge University Press, New York (1991)
  • \ref\key 4 R. Datko, On the integration of set valued mappings in Banach spaces , Fund. Math., 78 (1973), 205–208
  • \ref\key 5 N. Dunford and J. T. Schwartz, Linear operators, Part \rom1, Interscience Publishers, New York(1958) \ref\key 6
  • R. Kannan and D. O'Regan, A note on the solution set of integral inclusions , J. Integral Equations Appl., 12 (2000), 85–94 \ref\key 8
  • V. Lakshmikantham and S. Leela, Differential and Integral Inequalities, I , Academic Press, New York (1969) \ref\key 9
  • D. O'Regan, A note on the topological structure of the solution set of abstract Volterra equations , Proc. Roy. Irish Acad. Sect. A, 99 (1999), 67–74
  • \ref\key 10 C. Swartz, An introduction to functional analysis, Marcel Dekker, New York (1992)
  • \ref\key 11 S. Szufla, Set of fixed points of nonlinear mappings in function spaces , Funkcial. Ekvac., 22 (1979), 121–126