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Lower and Upper Solutions of Boundary Value Problems

  • Elvan Akin-Bohner
  • Ferhan Merdivenci Atici
  • Billûr Kaymakçalan

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].

Keywords

Lower Solution Extremal Solution Quadratic Convergence Monotone Sequence Iteration Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Elvan Akin-Bohner
    • 1
  • Ferhan Merdivenci Atici
    • 2
  • Billûr Kaymakçalan
    • 3
  1. 1.Department of Mathematics and StatisticsUniversity of Missouri-RollaRollaUSA
  2. 2.Department of MathematicsWestern Kentucky UniversityBowling GreenUSA
  3. 3.Department of Mathematics and Computer ScienceGeorgia Southern UniversityStatesboroUSA

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