Publication:
Existence and uniqueness of solutions to non-linear first order dynamic equations on time scales

dc.contributor.author Zaidi, Atiya-tul-Hussain en_US
dc.date.accessioned 2022-03-20T14:20:30Z
dc.date.available 2022-03-20T14:20:30Z
dc.date.issued 2009 en_US
dc.description.abstract The theory of dynamic equations on time scales provides an important bridge between the fields of differential and difference equations. It is particularly useful in describing phenomena that possess a hybrid continuous-discrete behaviour in their growth, like many temperate--2one insect populations and crops. A dynamic equation on a time scale is a generalised. 'two-in-one' model, it serves as a differential equation for purely continuous domains and as a difference equation for purely discrete ones. The field of "dynamic equations on time scales" is about 20 years old. As such, much of the basic (yet very important) linear theory has been established, however the non-linear extensions are yet to be fully developed. This thesis aims to fill this gap by providing the foundational framework of non-linear results from which further lines of inquiry can be launched. This thesis answers several important questions regarding the qualitative and quantitative properties of solutions to non-linear dynamic equations on time scales. Namely, (i) When do solutions exist? (ii) If solutions exist, then are they unique? (iii) How can such solutions be closely approximated? (iv) How can we explicitly solve certain problems to extract their solutions? The methods employed to address the above questions include: dynamic inequalities; iterative techniques and the method of successive approximations; and the fixed point approaches of Banach and Schauder. en_US
dc.identifier.uri http://hdl.handle.net/1959.4/44908
dc.language English
dc.language.iso EN en_US
dc.publisher UNSW, Sydney en_US
dc.rights CC BY-NC-ND 3.0 en_US
dc.rights.uri https://creativecommons.org/licenses/by-nc-nd/3.0/au/ en_US
dc.source Thesis Digitisation Program en_US
dc.subject.other Dynamic Equations en_US
dc.subject.other Non-Linear Results en_US
dc.title Existence and uniqueness of solutions to non-linear first order dynamic equations on time scales en_US
dc.type Thesis en_US
dcterms.accessRights open access
dcterms.rightsHolder Zaidi, Atiya-tul-Hussain
dspace.entity.type Publication en_US
unsw.accessRights.uri https://purl.org/coar/access_right/c_abf2
unsw.identifier.doi https://doi.org/10.26190/unsworks/14894
unsw.relation.faculty Science
unsw.relation.originalPublicationAffiliation Zaidi, Atiya-tul-Hussain, Mathematics & Statistics, Faculty of Science, UNSW en_US
unsw.relation.school School of Mathematics & Statistics *
unsw.thesis.degreetype PhD Doctorate en_US
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