Existence and uniqueness results for solutions to initial value problems in scales of Banach spaces: a thesis presented in partial fulfilment for the degree of Master of Science in Mathematics at Massey University

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dc.contributor.authorBulger, David Warren
dc.date.accessioned2019-04-18T01:01:12Z
dc.date.available2019-04-18T01:01:12Z
dc.date.issued1992
dc.description.abstractThis thesis addresses existence and uniqueness of solutions to certain classes of initial-value problems with functional differential equations. The technique of scales of Banach spaces is used. A scale of Banach spaces is a collection of Banach spaces varying on a real parameter. A scale consisting of function spaces can be used to suppress one variable in an initial-value problem in a partial differential equation of two independent variables, therefore enabling local existence and uniqueness of a solution to the problem to be shown with the classical method of successive apĀ­ proximations from the Picard-Lindelof Theorem of ordinary differential equations. Tuschke's presentation (c.f. [7]) of this technique and a related theorem has been adapted in Chapters 1 and 2. Chapters 3 and 4 present original theorems, stating existence and uniqueness of solutions to more general initial-value problems, having a retarded character.en_US
dc.identifier.urihttp://hdl.handle.net/10179/14529
dc.language.isoenen_US
dc.publisherMassey Universityen_US
dc.rightsThe Authoren_US
dc.subjectInitial value problemsen_US
dc.subjectBanach spacesen_US
dc.titleExistence and uniqueness results for solutions to initial value problems in scales of Banach spaces: a thesis presented in partial fulfilment for the degree of Master of Science in Mathematics at Massey Universityen_US
dc.typeThesisen_US
massey.contributor.authorBulger, David Warren
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorMassey Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Science (M. Sc.)en_US
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