Morris, Jason Robert
(2005)
Nonlinear ordinary and partial differential equations on unbounded domains.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
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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Details
Item Type: |
University of Pittsburgh ETD
|
Status: |
Unpublished |
Creators/Authors: |
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ETD Committee: |
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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: |
http://etd.library.pitt.edu/ETD/available/etd-03022005-112519/, etd-03022005-112519 |
Date Deposited: |
10 Nov 2011 19:31 |
Last Modified: |
15 Nov 2016 13:36 |
URI: |
http://d-scholarship.pitt.edu/id/eprint/6426 |
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