Nonlinear Resonance in Asymmetric Oscillators

We study the periodic solutions of equations with asymmetric nonlinearities “at resonance” with the Fu ík spectrum. We compute the associated topological degree and prove existence, multiplicity, and stability of large-amplitude oscillations for equations with a small friction term. Such equations can be viewed, e.g., as simple models for investigating vertical oscillations of long-span suspension bridges. The results are typically of a nonlinear nature, as some of the situations observed cannot occur with a linear equation.