Skip to main content
×
Home
    • Aa
    • Aa
  • Access
  • Cited by 3
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Ben Amar, Afif 2015. On an integral equation under Henstock–Kurzweil–Pettis integrability. Arabian Journal of Mathematics, Vol. 4, Issue. 2, p. 91.


    Li, Baolin and Gou, Haide 2015. On the Existence of Weak Solutions of Nonlinear Integral Equations in Banach Spaces. Mediterranean Journal of Mathematics,


    Aghajani, A. and Jalilian, Y. 2010. Existence and global attractivity of solutions of a nonlinear functional integral equation. Communications in Nonlinear Science and Numerical Simulation, Vol. 15, Issue. 11, p. 3306.


    ×
  • Bulletin of the Australian Mathematical Society, Volume 78, Issue 3
  • December 2008, pp. 507-522

THE SET OF SOLUTIONS OF INTEGRODIFFERENTIAL EQUATIONS IN BANACH SPACES

  • RAVI P. AGARWAL (a1), DONAL O’REGAN (a2) and ANETA SIKORSKA-NOWAK (a3)
  • DOI: http://dx.doi.org/10.1017/S0004972708000944
  • Published online: 01 December 2008
Abstract
Abstract

In this paper, we first prove an existence theorem for the integrodifferential equation (*)where f,k,x are functions with values in a Banach space E and the integral is taken in the sense of Henstock–Kurzweil–Pettis. In the second part of the paper we show that the set S of all solutions of the problem (*) is compact and connected in (C(Id,E),ω), where .

    • Send article to Kindle

      To send this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      THE SET OF SOLUTIONS OF INTEGRODIFFERENTIAL EQUATIONS IN BANACH SPACES
      Your Kindle email address
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      THE SET OF SOLUTIONS OF INTEGRODIFFERENTIAL EQUATIONS IN BANACH SPACES
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      THE SET OF SOLUTIONS OF INTEGRODIFFERENTIAL EQUATIONS IN BANACH SPACES
      Available formats
      ×
Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[3]R. P. Agarwal and D. O’Regan , ‘Existence results for singular integral equations of Fredholm type’, Appl. Math. Lett. 13(2) (2000), 2734.

[4]Z. Artstein , ‘Topological dynamics of ordinary differential equations and Kurzweil equations’, J. Differential Equations 23 (1977), 224243.

[8]T. S. Chew , ‘On Kurzweil generalized ordinary differential equations’, J. Differential Equations 76 (1988), 286293.

[10]M. Cichoń , ‘Convergence theorems for the Henstock–Kurzweil–Pettis integral’, Acta Math. Hungarica 92 (2001), 7582.

[11]M. Cichoń and I. Kubiaczyk , ‘On the set of solutions of the Cauchy problem in Banach spaces’, Arch. Math. 63 (1994), 251257.

[13]M. Cichoń , I. Kubiaczyk and A. Sikorska , ‘The Henstock–Kurzweil–Pettis integrals and existence theorems for the Cauchy problem’, Czechoslovak Math. J. 54 (2004), 279289.

[14]F. Cramer , V. Lakshmikantham and A. R. Mitchell , ‘On the existence of weak solution of differential equations in nonreflexive Banach spaces’, Nonlinear. Anal., TMA 2 (1978), 169177.

[15]R. F. Geitz , ‘Pettis integration’, Proc. Amer. Math. Soc. 82 (1991), 8186.

[18]R. A. Gordon , ‘Riemann integration in Banach spaces’, Rocky Mountain J. Math. 21 (1991), 923949.

[22]I. Kubiaczyk , ‘Kneser type theorems for ordinary differential equations in Banach spaces’, J. Differential Equations 45 (1982), 139146.

[25]M. Meehan and D. O’Regan , ‘Existence theory for nonlinear Volterra integrodifferential and integral equations’, Nonlinear Anal. TMA 31(3/4) (1998), 317341.

[27]D. O’Regan , ‘Existence results for nonlinear integral equations’, J. Math. Anal. Appl. 192(3) (1995), 705726.

[28]D. O’Regan and M. Meehan , Existence Theory for Integral and Integrodifferential Equations, Mathematics and Its Applications, 445 (Kluwer Academic, Dordrecht, 1998).

[29]B. J. Pettis , ‘On integration in vector spaces’, Trans. Amer. Math. Soc. 44 (1938), 277304.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords: