Abstract: We consider the quasilinear equation of the form
where is a positive C1 function defined in
and
has one zero at
, is non positive and not identically 0 in
, and is locally lipschitz, positive and satisfies some
superlinear growth assumption in
. We carefully study the
behaviour of solutions of the corresponding initial value problem for the
radial version of the quasilinear equation and combining, as Cortazar,
Felmer, and Elgueta, comparison arguments due to Coffman and Kwong, which
were thought to be restricted to the semilinear case only
, with some
separation techniques, we show that any zero of the solutions to the initial
value problem is monotone decreasing with respect to the initial value,
which leads immediately the uniqueness of positive radial ground states, and
the uniqueness of positive radial solutions of the Dirichlet problem on a
ball.
This article has been accepted to be published in Communications in Contemporary Mathematics.