Uniqueness of solutions of boundary value problems at resonance

Year 2018, Volume: 2 Issue: 3, 168 - 183, 30.09.2018

Jabr Aljedani , Paul Eloe

https://doi.org/10.31197/atnaa.453919

Cited By: 2

Abstract

In this paper, the method of upper and lower solutions is employed to obtain uniqueness of solutions for a boundary value problem at resonance.  The shift method is applied to show the existence of solutions.  A monotone iteration scheme is developed and sequences of approximate solutions are constructed that converge monotonically to the unique solution of the boundary value problem at resonance.  Two examples are provided in which explicit upper and lower solutions are exhibited.

Keywords

boundary value problem at resonance; shift method; upper and lower solutions; monotone convergence

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