EXACT RATE OF DECAY FOR SOLUTIONS TO DAMPED SECOND ORDER ODE'S WITH A DEGENERATE POTENTIAL

Abstract

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.

Keywords

• Rate of convergence to equilibrium
• second order equation with damping
• non-autonomous decay