Electron. J. Diff. Equ.,
Vol. 2016 (2016), No. 227, pp. 19.
Existence and nonexistence of solutions for semilinear 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
where f is odd with f<0 on
,
f>0 on
,
for
,
and where the function
K(r) is assumed to be positive and
as
.
The primitive
has a "hilltop" at
.
We prove that if
with
and if R>0 is sufficiently small then there are a finite number of
solutions of
on the exterior of the ball of
radius R such that
as
.
We also prove the
nonexistence of solutions if R is sufficiently large.
Submitted July 20, 2016. Published August 22, 2016.
Math Subject Classifications: 34B40, 35B05.
Key Words: Exterior domains; semilinear; superlinear; 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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