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Unbounded solutions of forced isochronous oscillators at resonance. (English) Zbl 1030.70011

Summary: We study the behavior of large amplitude solutions for forced nonlinear oscillators at resonance, the nonlinearity being a bounded perturbation of a function derived from an isochronous potential, i.e., a potential leading to free oscillations that all have the same period.

MSC:

70K30 Nonlinear resonances for nonlinear problems in mechanics
70K40 Forced motions for nonlinear problems in mechanics
34B15 Nonlinear boundary value problems for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
34C11 Growth and boundedness of solutions to ordinary differential equations
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