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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Positive solutions of $ q$-difference equation


Authors: Moustafa El-Shahed and H. A. Hassan
Journal: Proc. Amer. Math. Soc. 138 (2010), 1733-1738
MSC (2010): Primary 39A13, 45M20, 34B18, 34B27
Published electronically: December 16, 2009
MathSciNet review: 2587458
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Abstract: In this paper we investigate the existence of positive solutions of the $ q$-difference equation $ -D_q^2u(t)=a(t) f(u(t))$ with some boundary conditions by applying a fixed point theorem in cones.


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Additional Information

Moustafa El-Shahed
Affiliation: College of Education, P.O. Box 3771, Qasssim - Unizah, Kingdom of Saudi Arabia
Email: elshahedm@yahoo.com

H. A. Hassan
Affiliation: Department of Mathematics, Faculty of Basic Education, The Public Authority for Applied Education and Training, P.O. Box 23167, Kuwait
Email: hassanatef1@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10185-5
PII: S 0002-9939(09)10185-5
Keywords: Boundary-value problem, Krasnoselskii's fixed point theorem, Green's function, $q$-difference equation, positive solution.
Received by editor(s): April 27, 2009
Received by editor(s) in revised form: August 27, 2009
Published electronically: December 16, 2009
Communicated by: Varghese Mathai
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.