This paper surveys an area of nonlinear functional analysis and its applications. The main application is to the existence and multiplicity of periodic solutions of a possible mathematical models of nonlinearly supported bending beams, and their possible application to nonlinear behavior as observed in large-amplitude flexings in suspension bridges. A second area, periodic flexings in a floating beam, also nonlinearly supported, is covered at the end of the paper.

Large-amplitude periodic oscillations in suspension bridges: some new connections with nonlinear analysis

Infinite Dimensional Morse Theory and Multiple Solution Problems (K. C. Chang)

The effect of harmonic excitation on suspension bridges is examined as a first step towards the understanding of the effect of wind, and possibly certain kinds of earthquake, excitation on such structures. The Lazer-McKenna suspension bridge model is studied completely for the first time by using a methodology that has been successfully applied to models of rocking blocks and other free-standing rigid structures. An unexpectedly rich dynamical structure is revealed in this way. Conditions for the existence of asymptotic periodic responses are established, via a complicated nonlinear transcen- dental equation. A two-part Poincare map is derived to study the orbital stability of such solutions. Numerical results are presented which illustrate the application of the analytical procedure to find and classify stable and unstable solutions, as well as determine bifurcation points accurately. The richness of the possible dynamics is then illustrated by a menagerie of solutions which exhibit fold and flip bifurca...

A piecewise linear suspension bridge model : nonlinear dynamics and orbital continuation

Functional analysis : with applications

After recalling some preliminary notions from differential geometry, this chapter presents the local and global aspects of the theory of nondegenerate critical manifolds. These manifolds are a natural extension of the notion of non-degenerate critical point.

Nondegenerate Critical Manifolds

Controllability of nonlinear neutral evolution integrodifferential systems

Multiplicity of solutions and source terms in a fourth order nonlinear elliptic equation

Let ω be a bounded open set in Rn with smooth boundary ϖω We are concerned with a fourth order semilinear elliptic boundary value problem Δ2u + cΔu = bu+ + s inω under Dirichlet boundary condition. We investigate the existence of solutions of the fourth order nonlinear equation (0.1) when the nonlinearity bu+ crosses eigenvalues of Δ2 + cΔ under Dirichlet boundary condition.

Q-Heung Choi

Papers

Controllability of nonlinear neutral evolution integrodifferential systems

Multiplicity of solutions and source terms in a fourth order nonlinear elliptic equation

Multiplicity results on a nonlinear biharmonic equation

Multiplicity Results on a Fourth Order Nonlinear Elliptic Equation

On periodic solutions of the nonlinear suspension bridge equation