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Generalized monotone iterative technique for set differential equations involving causal operators with memory

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Abstract

Using the method of lower and upper solutions and the monotone iterative technique for the linear differential equations involving anticipation and retardation, we develop the generalized monotone iterative technique for the set differential equations involving causal operators with memory.

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References

  1. Corduneanu, C.: Functional Equations with Causal Operators. Taylor and Francis, Newyork (2003)

  2. Drici, Z., McRae, F.A., Vasundhara Devi, J.: Differential equations with causal operators in a Banach space. Nonlinear Anal. 62(2), 301–313 (2005)

    Google Scholar 

  3. Drici, Z., McRae, F.A., Vasundhara Devi, J.: Set differential equations with causal operators. Math. Probl. Eng. 2, 185–194 (2005)

    Google Scholar 

  4. Drici, Z., McRae, F.A., Vasundhara Devi, J.: Stability results for set differential equations with causal maps. Dyn. Syst. Appl. 15, 451–464 (2006)

    Google Scholar 

  5. Drici, Z., McRae, F.A., Vasundhara Devi, J.: Monotone iterative technique for PBVP involving causal operators. Nonlinear Anal. 64 1271–1277 (2006)

    Google Scholar 

  6. Gnana Bhaskar, T., Lakshmikantham, V., Vasundhara Devi, J.: Monotone iterative technique for functional differential equations with retardation and anticipation. Nonlinear Anal. 66, 2237–2242 (2006)

    Google Scholar 

  7. Ladde, G.S., Lakshmikantham, V., Vatsala, A.S.: Monotone Iterative Technique for Nonlinear Differential equations. Pittman Publishing Inc, London (1985)

  8. Lakshmikantham, V., Leela, S.: Differential and Integral Inequalities, vol. I and II. Academic press, New York (1969)

  9. Lakshmikantham, V., Rama Mohan Rao, M.: Theory of Integro Differential Equations. Gordan and Breach Science Publishers, Amsterdam (1995)

  10. Lakshmikantham, V., Koksal, S.: Monotone Flows and Rapid Convergence for Nonlinear Partial Differential Equations. Taylor and Francis, London (2003)

  11. Lakshmikantham, V., Gnana Bhaskar, T., Vasundhara Devi, J.: Theory of Set Differential Equations in Metric Spaces. Cambridge Scientific Publishers (2006)

  12. Lakshmikantham, V., Leela, S., Drici, Z., McRae, F.A.: Theory of Causal Differential Equations. Atlantis Press and World Scientific, Paris (2009)

  13. Vasundhara Devi, J., Sreedhar, Ch.V., Nagamani, S.: Monotone iterative technique for integro differential equations with retardation and anticipation. Commun. Appl. Anal. 14(0.3 and 4), 325–336 (2010)

    Google Scholar 

  14. Vasundhra Devi, J.: Comparison theorems and existence results for set causal operators with memory. Nonlinear Stud. (submitted)

  15. Vasundhara Devi, J.: Existence and uniqueness results for solutions of set differential equations involving causal operators with memory European. J. Pure Appl. Math. 3(0.4), 737–747 (2010)

    Google Scholar 

  16. Vasundhara Devi, J.: Extremal solutions and continuous dependence for set differential equations involving causal operators with memory. Commun. Appl. Anal. 15(0.1), 113–124 (2011)

    Google Scholar 

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Acknowledgements

This work has been done under the project no. SR/S4/MS: 491/07 sanctioned by Department of Science and Technology, Government of India. The authors acknowledges their support.

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  1. Department of Mathematics, GVP—Prof. V.Lakshmikantham Institute for Advanced Studies, GVP College of Engineering, Visakhapatnam, Andhra Pradesh, India

    J. Vasundhara Devi

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Correspondence to J. Vasundhara Devi.

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Vasundhara Devi, J. Generalized monotone iterative technique for set differential equations involving causal operators with memory. Int J Adv Eng Sci Appl Math 3, 74–83 (2011). https://doi.org/10.1007/s12572-011-0031-1

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  • DOI: https://doi.org/10.1007/s12572-011-0031-1

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