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].
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© 2003 Springer Science+Business Media New York
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Akin-Bohner, E., Atici, F.M., Kaymakçalan, B. (2003). Lower and Upper Solutions of Boundary Value Problems. In: Bohner, M., Peterson, A. (eds) Advances in Dynamic Equations on Time Scales. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8230-9_6
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DOI: https://doi.org/10.1007/978-0-8176-8230-9_6
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6502-3
Online ISBN: 978-0-8176-8230-9
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