Uniqueness of solutions of boundary value problems at resonance

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Advances in the Theory of Nonlinear Analysis and its Application
Volume:2 Issue:3
Uniqueness of solutions of boundary value problems at resonance

Uniqueness of solutions of boundary value problems at resonance

Authors : Jabr ALJEDANİ, Paul ELOE

Pages : 168-183

Doi:10.31197/atnaa.453919

View : 47 | Download : 8

Publication Date : 2018-09-30

Article Type : Research Paper

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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