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

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.