  Oscillons are long-lived, localized, oscillatory scalar field configurations.
In this work we derive a condition for the existence of small-amplitude
oscillons (and provide solutions) in scalar field theories with non-canonical
kinetic terms. While oscillons have been studied extensively in the canonical
case, this is the first example of oscillons in scalar field theories with
non-canonical kinetic terms. In particular, we demonstrate the existence of
oscillons supported solely by the non-canonical kinetic terms, without any need
for nonlinear terms in the potential. In the small-amplitude limit, we provide
an explicit condition for their stability in d+1 dimensions against
long-wavelength perturbations. We show that for d > 2, there exists a
long-wavelength instability which can lead to radial collapse of
small-amplitude oscillons.
