# American Institute of Mathematical Sciences

December  2018, 7(4): 531-543. doi: 10.3934/eect.2018025

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

 Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic

Received  June 2017 Revised  May 2018 Published  September 2018

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.

Citation: Tomáš Bárta. Exact rate of decay for solutions to damped second order ODE's with a degenerate potential. Evolution Equations & Control Theory, 2018, 7 (4) : 531-543. doi: 10.3934/eect.2018025
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