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Nonlinear Boundary Value Problems

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500 Examples and Problems of Applied Differential Equations

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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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Authors and Affiliations

  1. Department of Mathematics, Texas A&M University–Kingsville, Kingsville, TX, USA

    Ravi P. Agarwal & Simona Hodis

  2. Department of Mathematics, National University of Ireland, Galway, Ireland

    Donal O’Regan

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  1. Ravi P. Agarwal
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  2. Simona Hodis
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  3. Donal O’Regan
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Correspondence to Ravi P. Agarwal .

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Agarwal, R.P., Hodis, S., O’Regan, D. (2019). Nonlinear Boundary Value Problems. In: 500 Examples and Problems of Applied Differential Equations. Problem Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-26384-3_9

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