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Lower and Upper Solutions of Boundary Value Problems

In: Advances in Dynamic Equations on Time Scales

Author

Listed:
  • Elvan Akin-Bohner

    (University of Missouri-Rolla, Department of Mathematics and Statistics)

  • Ferhan Merdivenci Atici

    (Western Kentucky University, Department of Mathematics)

  • Billûr Kaymakçalan

    (Georgia Southern University, Department of Mathematics and Computer Science)

Abstract

The method of lower and upper solutions, coupled with the monotone iterative technique provides an effective and flexible mechanism that offers theoretical as well as constructive existence results for nonlinear problems in a closed set which is generated by the lower and upper solutions. The lower and upper solutions serve as bounds for solutions which are improved by a monotone iterative process. The ideas imbedded in this technique have proved to be of immense value and have played an important rôle in unifying a variety of nonlinear problems. A comprehensive introduction to the monotone iterative techniques is given by Ladde, Lakshmikantham and Vatsala in [196].

Suggested Citation

  • Elvan Akin-Bohner & Ferhan Merdivenci Atici & Billûr Kaymakçalan, 2003. "Lower and Upper Solutions of Boundary Value Problems," Springer Books, in: Martin Bohner & Allan Peterson (ed.), Advances in Dynamic Equations on Time Scales, chapter 0, pages 165-188, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-8230-9_6
    DOI: 10.1007/978-0-8176-8230-9_6
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