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Positive solutions of  -difference equation
Author(s):
Moustafa
El-Shahed;
H.
A.
Hassan
Journal:
Proc. Amer. Math. Soc.
138
(2010),
1733-1738.
MSC (2010):
Primary 39A13, 45M20, 34B18, 34B27
Posted:
December 16, 2009
MathSciNet review:
2587458
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Abstract:
In this paper we investigate the existence of positive solutions of the  -difference equation  with some boundary conditions by applying a fixed point theorem in cones.
References:
-
- 1.
- M. H. Annaby and Z. S. Mansour,
 -Taylor and interpolation series for Jackson  -difference operators, Journal of Mathematical Analysis and Applications, 344: 472-483, 2008. MR 2416321 (2009b:33020) - 2.
- L.H. Erbe and H. Wang,
On the existence of positive solutions of ordinary differential equations. Proc. Amer. Math. Soc., 120: 743-748, 1994. MR 1204373 (94e:34025) - 3.
- G. Gasper and M. Rahmen, Basic Hypergeometric Series, Cambridge University Press, Cambridge, 2004. MR 2128719 (2006d:33028)
- 4.
- D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, San Diego, 1988. MR 959889 (89k:47084)
- 5.
- F.H. Jackson,
On  -definite integrals.
Quart. J. Pure and Appl. Math., 41: 193-203, 1910. - 6.
- M. A. Krasnoselskii,
Positive Solutions of Operator Equations,
Noordhoff, Groningen, 1964. MR 0181881 (31:6107) - 7.
- M. K. Kwong,
On Krasnoselskii's cone fixed point theorem.
Fixed Point Theory and Applications, 2008, Art. ID 164537, 1-18. MR 2395322 (2009d:47066) - 8.
- S. D. Marinković, P. M. Rajković and M. Stanković,
The Linear  -Differential Equation and  -Holonomic Functions,
XVII Conference on Applied Mathematics, D. Herceg, H. Zarin, eds.; Department of Mathematics and Informatics, Novi Sad, 2007, 13-20.
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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:
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
Posted:
December 16, 2009
Communicated by:
Varghese Mathai
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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