Nonautonomous and nonlinear effects in generalized classical oscillators: A boundedness theorem

The boundedness of the amplitude and energy of the oscillators is analyzed in relation to the phenomenon of exponential instability, arising in certain nonautonomous linear oscillators. The oscillating nature of the solutions, characterized by the symmetric potentials with only one equilibrium point are also studied. The presence of a quadratically diverging autonomous part in the potential, is also observed.