Arabian Journal of Mathematics

, Volume 8, Issue 1, pp 43–53 | Cite as

On a third-order boundary value problem at resonance on the half-line

  • S. A. IyaseEmail author
Open Access


In this paper, we establish existence of solutions for the following boundary value problem on the half-line: \((q(t)u''(t))' = g(t, u(t), u'(t), u''(t)),\;\;\; t \in (0, \infty )\) subject to the boundary conditions \( u'(0) = \sum ^{m}_{i=1}\alpha _i\int ^{\xi _i}_0 u(t)\mathrm{d}t, u(0) = 0,\; \lim _{t\rightarrow \infty }q(t)u''(t)=0.\) We establish sufficient conditions for the existence of at least one solution using coincidence degree arguments. An example is provided to validate our result.

Mathematics Subject Classification

34B10 34B15 34B45 



The author wishes to express his gratitude to the anonymous referees for their useful suggestions and corrections.


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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of MathematicsCovenant University OtaOtaNigeria

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