Positive solutions of $q$-difference equation
HTML articles powered by AMS MathViewer
- by Moustafa El-Shahed and H. A. Hassan PDF
- Proc. Amer. Math. Soc. 138 (2010), 1733-1738 Request permission
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.References
- M. H. Annaby and Z. S. Mansour, $q$-Taylor and interpolation series for Jackson $q$-difference operators, J. Math. Anal. Appl. 344 (2008), no.Ā 1, 472ā€“483. MR 2416321, DOI 10.1016/j.jmaa.2008.02.033
- L. H. Erbe and Haiyan Wang, On the existence of positive solutions of ordinary differential equations, Proc. Amer. Math. Soc. 120 (1994), no.Ā 3, 743ā€“748. MR 1204373, DOI 10.1090/S0002-9939-1994-1204373-9
- George Gasper and Mizan Rahman, Basic hypergeometric series, 2nd ed., Encyclopedia of Mathematics and its Applications, vol. 96, Cambridge University Press, Cambridge, 2004. With a foreword by Richard Askey. MR 2128719, DOI 10.1017/CBO9780511526251
- Da Jun Guo and V. Lakshmikantham, Nonlinear problems in abstract cones, Notes and Reports in Mathematics in Science and Engineering, vol. 5, Academic Press, Inc., Boston, MA, 1988. MR 959889
- F.H. Jackson, On $q$-definite integrals. Quart. J. Pure and Appl. Math., 41: 193ā€“203, 1910.
- M. A. Krasnoselā€²skiÄ, Positive solutions of operator equations, P. Noordhoff Ltd., Groningen, 1964. Translated from the Russian by Richard E. Flaherty; edited by Leo F. Boron. MR 0181881
- Man Kam Kwong, On Krasnoselskiiā€™s cone fixed point theorem, Fixed Point Theory Appl. , posted on (2008), Art. ID 164537, 18. MR 2395322, DOI 10.1155/2008/164537
- S. D. Marinković, P. M. Rajković and M. Stanković, The Linear $q$-Differential Equation and $q$-Holonomic Functions, XVII Conference on Applied Mathematics, D. Herceg, H. Zarin, eds.; Department of Mathematics and Informatics, Novi Sad, 2007, 13ā€“20.
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
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 1733-1738
- MSC (2010): Primary 39A13, 45M20, 34B18, 34B27
- DOI: https://doi.org/10.1090/S0002-9939-09-10185-5
- MathSciNet review: 2587458