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Nonlinear resonance in asymmetric oscillators. (English) Zbl 0915.34033

Periodic solutions to equations with asymmetric nonlinearities at resonance with Fučik spectrum are studied. The associated topological degree is computed and existence, multiplicity, and stability of large-amplitude oscillations are proved for an equation with small friction term. The considered equations can be viewed as simple models for investigating vertical oscillations of long-span suspension bridges.

MSC:

34C25 Periodic solutions to ordinary differential equations
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