Document Type

Article

Publication Date

10-2019

Publication Source

Georgian Mathematical Journal

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.

ISBN/ISSN

1572-9176

Document Version

Published Version

Comments

Document is made available for download with the permission of the author in compliance with the publisher's policy on self-archiving. Permission documentation is on file.

Publisher

De Gruyter

Volume

28

Issue

2

Peer Reviewed

yes

Keywords

Boundary value problem at resonance, shift method, upper and lower solutions, quasilinearization

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