Skip to main content

Comparison theorem and its applications

  • Chapter
General Inequalities 6

Abstract

By developing comparison theorems for stochastic integro-differential equations, stability and error estimate problems are investigated. The obtained results provide the information about random environmental perturbations. In particular, the presented work provides a partial solution to the problem of “Stochastic versus Deterministic” in the modelling of dynamic systems in biological, engineering, and physical sciences. Examples are given to show the scope of the results.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A.T. Bharucha-Reid, Random Integral Equations. Academic Press, New York, 1972.

    Google Scholar 

  2. J. Chandra, G.S. Ladde and V. Lakshmikantham, On the fundamental theory of nonlinear second order stochastic boundary value problems. Stoch. Anal. Appl. 1 (1983), 1–19.

    Article  Google Scholar 

  3. J. Chandra, G.S. Ladde and V. Lakshmikantham, Stochastic analysis of compressible gas lubricated slider bearing problem. SIAM J. Appl. Math. 43 (1983), 1174–1186.

    Google Scholar 

  4. G.S. Ladde and V. Lakshmikantham, Random Differential Inequalities. Academic Press, New York, 1980.

    Google Scholar 

  5. G.S. Ladde, V. Lakshmikantham and M. Sambandham, Comparison Theorem and Error Estimates of Stochastic Differential Systems. Stoch. Anal. Appl. 3 (1) (1985), 23–62.

    Article  Google Scholar 

  6. G.S. Ladde and S. Sathananthan, Itd-type systems of stochastic integro-differential equations. Integral Methods in Science and Engineering–90, Hemisphere Publ. Comp. (1991), pp. 75–89.

    Google Scholar 

  7. G.S. Ladde and S. Sathananthan, Error Estimates and Stability of Itd-type systems of Nonlinear Stochastic Integro-Differential Equations. Applicable Analysis. To appear.

    Google Scholar 

  8. V. Lakshmikantham, Some problems in integro-differential equations of Volterra type. J. Int. Eqs. 10 (1985), 137–146.

    Google Scholar 

  9. V. Lakshmikantham and S. Leela, Differential and Integral Inequalities. Academic Press, New York, 1968.

    Google Scholar 

  10. V. Lakshmikantham, S. Leela and A.A. Martynuk, Stability Analysis of Nonlinear Systems. Marcel Dekker, New York and Basel, 1989.

    Google Scholar 

  11. H.L. Royden, Real Analysis. Macmillan, 1968.

    Google Scholar 

  12. G.R. Shendge, A new approach to the stability theory of functional differential equations. J. Math. Anal. Appl. 95 (1983), 319–334.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer Basel AG

About this chapter

Cite this chapter

Ladde, G.S., Sambandham, M., Sathananthan, S. (1992). Comparison theorem and its applications. In: Walter, W. (eds) General Inequalities 6. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 103. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7565-3_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-7565-3_25

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-7567-7

  • Online ISBN: 978-3-0348-7565-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics