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# Exact rate of decay for solutions to damped second order ODE's with a degenerate potential

• We prove exact rate of decay for solutions to a class of second order ordinary differential equations with degenerate potentials, in particular, for potential functions that grow as different powers in different directions in a neigborhood of zero. As a tool we derive some decay estimates for scalar second order equations with non-autonomous damping.

Mathematics Subject Classification: Primary: 34D05, 34C10.

 Citation:

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