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  • Bulletin of the Australian Mathematical Society, Volume 82, Issue 1
  • August 2010, pp. 139-155

EXISTENCE OF RESOLVENT FOR VOLTERRA INTEGRAL EQUATIONS ON TIME SCALES

  • MURAT ADıVAR (a1) and YOUSSEF N. RAFFOUL (a2)
  • DOI: http://dx.doi.org/10.1017/S0004972709001166
  • Published online: 01 March 2010
Abstract
Abstract

We introduce the concept of ‘shift operators’ in order to establish sufficient conditions for the existence of the resolvent for the Volterra integral equation on time scales. The paper will serve as the foundation for future research on the qualitative analysis of solutions of Volterra integral equations on time scales, using the notion of the resolvent.

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Corresponding author
For correspondence; e-mail: murat.adivar@ieu.edu.tr
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This work was supported by the Scientific and Technological Research Council of Turkey.

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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.

[2]M. Bohner and G. Guseinov , ‘Riemann and Lebesgue integration’, Advances in Dynamic Equations on Time Scales (Birkhäuser, Boston, MA, 2003).

[4]M. Bohner and G. Guseinov , ‘Double integral calculus of variations on time scales’, Comput. Math. Appl. 54(1) (2007), 4557.

[5]M. Bohner and A. Peterson , ‘Dynamic equations on time scales’, An Introduction with Applications (Birkhäuser, Boston, MA, 2001).

[7]S. Hilger , ‘Analysis on measure chains: a unified approach to continuous and discrete calculus’, Results Math. 18 (1990), 1856.

[11]C. C. Tisdell and A. Zaidi , ‘Basic qualitative and quantitative results for solutions to nonlinear, dynamic equations on time scales with an application to economic modelling’, Nonlinear Anal. 68(11) (2008), 35043524.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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