Electron. J. Differential Equations,
Vol. 2017 (2017), No. 214, pp. 113.
Existence and nonexistence of solutions for sublinear equations
on exterior domains
Joseph A. Iaia
Abstract:
In this article we study radial solutions of
on
the exterior of the ball of radius R>0,
, centered at the origin
in
with u=0 on
where f is odd with
f<0 on
, f>0 on
,
with
0<p<1 for large u and
for large r.
We prove that if N>2 and
with
then there are no solutions with
for sufficiently
large R>0. On the other hand, if
and
k, n are nonnegative integers with
then there exist solutions,
, with k zeros on
and
if R>0 is sufficiently small.
Submitted December 29, 2016. Published September 13, 2017.
Math Subject Classifications: December 29, 2016. Published September 13, 2017.
Key Words: Exterior domains; semilinear; sublinear; radial.
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Joseph A. Iaia
Department of Mathematics
University of North Texas
P.O. Box 311430
Denton, TX 762031430, USA
email: iaia@unt.edu

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