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Nonlinear ordinary and partial differential equations on unbounded domains

Morris, Jason Robert (2005) Nonlinear ordinary and partial differential equations on unbounded domains. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Solutions are shown to exist for a variety of differential equations. Both ordinary and partial differential equations are considered, with specified initial conditions, boundary conditions, or simultaneous initial and boundary conditions. A key feature of the these problems is a condition at infinity; it is demanded that solutions decay towards zero as the temporal variable becomes arbitrarily large. This feature removes from the problem a certain compactness property, which precludes the use of traditional methods which employ the Leray-Schauder topological degree. This difficulty is overcome by use of a much newer theory of topological degree, developed by Fitzpatrick, Pejsachowicz and Rabier in 1992, and later developed further by Pejsachowicz and Rabier in 1998. This degree theory requires several properties in lieu of compactness. It is shown that these properties are available in a wide range of problems, and that there is a practical way to verify this fact in specific cases. Specific examples are given.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Morris, Jason
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairRabier, Patrick J.rabier@pitt.eduRABIER
Committee MemberLennard, Christopher J.lennard@pitt.eduLENNARD
Committee MemberMcLeod, J. Brycemcleod@pitt.eduMCLEOD
Committee MemberManfredi, Juan J.manfredi@pitt.eduMANFREDI
Committee MemberMizel, Victor
Date: 3 June 2005
Date Type: Completion
Defense Date: 17 March 2005
Approval Date: 3 June 2005
Submission Date: 2 March 2005
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: boundary value problem; exponential dichotomy; Fredholm operator; initial value problem; parabolic evolution equation; topological degree
Other ID:, etd-03022005-112519
Date Deposited: 10 Nov 2011 19:31
Last Modified: 15 Nov 2016 13:36


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