Quasilinearization and boundary value problems at resonance-Reference-Cited by-同舟云学术

Quasilinearization and boundary value problems at resonance

Published:2019-10-06 Issue:2 Volume:28 Page:173-184
ISSN:1572-9176
Container-title:Georgian Mathematical Journal
language:en
Short-container-title:

Author:

Alanazi Kareem¹,Alshammari Meshal²,Eloe Paul³^ORCID

Affiliation:

1. Department of Mathematics , College of Science and Arts , Aljouf University , El-Qurayat , Saudi Arabia

2. Department of Mathematics , Aljouf College of Technology , Al-Jawf , Saudi Arabia

3. Department of Mathematics , University of Dayton , Dayton , OH 45469-2316 , USA

Abstract

Abstract A quasilinearization algorithm is developed for boundary value problems at resonance. To do so, a standard monotonicity condition is assumed to obtain the uniqueness of solutions for the boundary value problem at resonance. Then the method of upper and lower solutions and the shift method are applied to obtain the existence of solutions. A quasilinearization algorithm is developed and sequences of approximate solutions are constructed, which converge monotonically and quadratically to the unique solution of the boundary value problem at resonance. Two examples are provided in which explicit upper and lower solutions are exhibited.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

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