will be considered in an exterior domain Ω ⊂ Rn, n ≥ 2, where f is nonnegative and
locally Hölder continuous in Ω × (0,∞). One objective is to find sharp necessary
conditions for (1) to be oscillatory in Ω under the sublinear hypothesis that
max|x|=rt−1f(x,t) is a nonincreasing function of t in (0,∞) for each fixed r > 0. The
necessary conditions below are proved in §2:
∫∞rmax|x|=rf(x,clogr)dr
= +∞
if n = 2;
∫∞rmax|x|=rf(x,c)dr
= +∞
if n ≥ 3
for some positive constant c. Sufficient conditions for (1) to be oscillatory in Ω are
proved in §3 under a modified sublinear hypothesis. These results are then combined
to yield characterizations of oscillatory sublinear equations of the Emden-Fowler type
in exterior domains.
