Uniqueness of solutions of boundary value problems at resonance

Open Access

Original research article

Author(s):

Jabr Aljedani^a, Paul Eloe^b

^a Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
^b Department of Mathematics, University of Dayton, Dayton, USA

Advances in the Theory of Nonlinear Analysis and its Applications 2(3), 168-183.

Received: August 15, 2018

Accepted: August 20, 2018

Published: August 22, 2018

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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APA Style

Aljedani, J., & Eloe, P. (2018). Uniqueness of solutions of boundary value problems at resonance. Advances in the Theory of Nonlinear Analysis and its Application, 2(3), 168-183.