Abstract/Details

Numerical and theoretical results on large-amplitude periodic solutions of a suspension bridge equation

Humphreys, Lisa Doolittle. 
 University of Connecticut ProQuest Dissertations Publishing,  1994. 9513871.

Abstract (summary)

We are interested in periodic solutions of the Lazer-McKenna suspension bridge model$$u\sb{tt} + u\sb{xxxx} + bu\sp+ = 1 + \delta h(x,t)$$with hinged-end boundary conditions. Appropriate restrictions are placed on h(x,t) and $\delta$, while solutions are sought in the usual symmetric subspace of $L\sp2$. The dissertation is then comprised of two main parts. First, the known result of three distinct solutions for $3 < b < 15$ is reproduced using a degree theoretic argument. This foundation allows us to then show the existence of an $\epsilon > 0$ so that when $15 < b \leq 15 + \epsilon$, four distinct solutions result. Secondly, the model is investigated numerically using an algorithm based on a constructive implementation of the mountain pass theorems of Rabinowitz and Ekeland.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences
Title
Numerical and theoretical results on large-amplitude periodic solutions of a suspension bridge equation
Author
Humphreys, Lisa Doolittle
Number of pages
67
Degree date
1994
School code
0056
Source
DAI-B 55/12, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
979-8-209-22869-1
Advisor
McKenna, Patrick
University/institution
University of Connecticut
University location
United States -- Connecticut
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
9513871
ProQuest document ID
304142073
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/304142073/abstract