On positive solutions for singular boundary value problems of differential and difference equations / Noor Halimatus Sa'diah Ismail

This thesis is concerned with the existence and multiplicity of positive solutions to singular boundary value problems (BVPs) of differential and difference equations. By using the Krasnoselskii fixed point theorem on compression and expectation in cone, sufficient conditions for the existence of po...

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Main Author:	Ismail, Noor Halimatus Sa'diah
Format:	Thesis
Language:	English
Published:	2016
Subjects:	Algebra
Online Access:	https://ir.uitm.edu.my/id/eprint/17873/1/TM_NOOR%20HALIMATUS%20SA%27DIAH%20ISMAIL%20CS%2016_5.pdf
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spelling	my-uitm-ir.178732019-03-12T08:02:53Z On positive solutions for singular boundary value problems of differential and difference equations / Noor Halimatus Sa'diah Ismail 2016 Ismail, Noor Halimatus Sa'diah Algebra This thesis is concerned with the existence and multiplicity of positive solutions to singular boundary value problems (BVPs) of differential and difference equations. By using the Krasnoselskii fixed point theorem on compression and expectation in cone, sufficient conditions for the existence of positive solutions are established for a singular system of first-order differential equations and singular second-order BVPs of difference equations. Our results give an almost complete structure of the existence of positive solutions for the problems studied with an appropriately chosen parameter. By choosing appropriate cone, the singularity of the equations is essentially removed and the associated positive operator becomes well defined for certain ranges of functions even when et is negative. By employing the Krasnoselskii fixed point theorem in cone, the existence and multiplicity of positive periodic solutions for a singular system of first-order ordinary differential equations is established. As an extension, the discrete analogue of singular differential problems of second-order BVPs with a parameter is derived. The existence of positive solutions is obtained by applying the Krasnoselskii fixed point theorem in cone. The result is then extended to a singular discrete system of second-order two point BVPs. Also the existence of positive solutions is investigated for a singular discrete system of second-order multi-point BVPs. 2016 Thesis https://ir.uitm.edu.my/id/eprint/17873/ https://ir.uitm.edu.my/id/eprint/17873/1/TM_NOOR%20HALIMATUS%20SA%27DIAH%20ISMAIL%20CS%2016_5.pdf text en public mphil masters Universiti Teknologi MARA Faculty of Computer and Mathematical Sciences
institution	Universiti Teknologi MARA
collection	UiTM Institutional Repository
language	English
topic	Algebra
spellingShingle	Algebra Ismail, Noor Halimatus Sa'diah On positive solutions for singular boundary value problems of differential and difference equations / Noor Halimatus Sa'diah Ismail
description	This thesis is concerned with the existence and multiplicity of positive solutions to singular boundary value problems (BVPs) of differential and difference equations. By using the Krasnoselskii fixed point theorem on compression and expectation in cone, sufficient conditions for the existence of positive solutions are established for a singular system of first-order differential equations and singular second-order BVPs of difference equations. Our results give an almost complete structure of the existence of positive solutions for the problems studied with an appropriately chosen parameter. By choosing appropriate cone, the singularity of the equations is essentially removed and the associated positive operator becomes well defined for certain ranges of functions even when et is negative. By employing the Krasnoselskii fixed point theorem in cone, the existence and multiplicity of positive periodic solutions for a singular system of first-order ordinary differential equations is established. As an extension, the discrete analogue of singular differential problems of second-order BVPs with a parameter is derived. The existence of positive solutions is obtained by applying the Krasnoselskii fixed point theorem in cone. The result is then extended to a singular discrete system of second-order two point BVPs. Also the existence of positive solutions is investigated for a singular discrete system of second-order multi-point BVPs.
format	Thesis
qualification_name	Master of Philosophy (M.Phil.)
qualification_level	Master's degree
author	Ismail, Noor Halimatus Sa'diah
author_facet	Ismail, Noor Halimatus Sa'diah
author_sort	Ismail, Noor Halimatus Sa'diah
title	On positive solutions for singular boundary value problems of differential and difference equations / Noor Halimatus Sa'diah Ismail
title_short	On positive solutions for singular boundary value problems of differential and difference equations / Noor Halimatus Sa'diah Ismail
title_full	On positive solutions for singular boundary value problems of differential and difference equations / Noor Halimatus Sa'diah Ismail
title_fullStr	On positive solutions for singular boundary value problems of differential and difference equations / Noor Halimatus Sa'diah Ismail
title_full_unstemmed	On positive solutions for singular boundary value problems of differential and difference equations / Noor Halimatus Sa'diah Ismail
title_sort	on positive solutions for singular boundary value problems of differential and difference equations / noor halimatus sa'diah ismail
granting_institution	Universiti Teknologi MARA
granting_department	Faculty of Computer and Mathematical Sciences
publishDate	2016
url	https://ir.uitm.edu.my/id/eprint/17873/1/TM_NOOR%20HALIMATUS%20SA%27DIAH%20ISMAIL%20CS%2016_5.pdf
_version_	1783733615483420672

On positive solutions for singular boundary value problems of differential and difference equations / Noor Halimatus Sa'diah Ismail

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