Document Type

Article

Publication Date

6-14-2016

Publication Source

Electronic Journal of Qualitative Theory of Differential Equations

Abstract

We consider two simple boundary value problems at resonance for an ordinary differential equation. Employing a shift argument, a regular fixed point operator is constructed. We employ the monotone method coupled with a method of upper and lower solutions and obtain sufficient conditions for the existence of solutions of boundary value problems at resonance for nonlinear boundary value problems. Three applications are presented in which explicit upper solutions and lower solutions are exhibited for the first boundary value problem. Two applications are presented for the second boundary value problem. Of interest, the upper and lower solutions are easily and explicitly constructed. Of primary interest, the upper and lower solutions are elements of the kernel of the linear problem at resonance.

Inclusive pages

1-13

ISBN/ISSN

1417-3875

Document Version

Published Version

Comments

This document has been made available for download in accordance with the publisher's policy on open access.

DOI: https://doi.org/10.14232/ejqtde.2016.1.40

Permission documentation on file.

Publisher

Bolyai Institute, University of Szeged and the Hungarian Academy of Sciences

Volume

40

Volume

40

Peer Reviewed

yes


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