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Nonlinear Boundary Value Problems

  • Ravi P. AgarwalEmail author
  • Simona Hodis
  • Donal O’Regan
Chapter
First Online:
Part of the Problem Books in Mathematics book series (PBM)

Abstract

In this chapter, mainly we shall show the importance of the method of upper and lower solutions [6, 13, 22, 24] to nonlinear boundary value problems which appear in real-world phenomena. The main advantage of this method is that besides proving the existence of the solutions it also provides upper and lower bounds on the solutions. These bounds are of immense value in numerical computations of the solutions [99, 100, 101].

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ravi P. Agarwal
    • 1
    Email author
  • Simona Hodis
    • 1
  • Donal O’Regan
    • 2
  1. 1.Department of MathematicsTexas A&M University–KingsvilleKingsvilleUSA
  2. 2.Department of MathematicsNational University of IrelandGalwayIreland

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