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Summary: A NOTE ON THE DYNAMICS OF AN OSCILLATOR
IN THE PRESENCE OF STRONG FRICTION
H. AMANN AND J.I. DIAZ
Abstract. We study the longtime behavior of the solutions of a second order
autonomous differential equation, differing from the one of a harmonic oscilla-
tor by a nonlinear friction term being only H¨older continuous. In particular,
we show that there are two solution curves reaching the rest point in finite
time.
Introduction
In this note we study the phase plane flow of the equation
¨x + ( x) + x = 0, (0.1)
with the friction function possessing the following properties:
it is continuous on R and locally Lipschitz continuous on R\{0},
odd, and positive for positive arguments;
there exist a, > 0 and (0, 1) such that () = a
for 0 < ;
lim
()/ < 1/2.
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