Electron. J. Differential Equations, Vol. 2020 (2020), No. 117, pp. 116.
Existence and nonexistence of radial solutions for
semilinear equations with bounded nonlinearities on exterior domains
Joseph 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
. With mild assumptions on f we prove that if
with
then there are n solutions of
on the exterior of the ball of radius R such that
as
if R>0 is sufficiently small. We also show there are no solutions
if R>0 is sufficiently large.
Submitted January 6, 2020. Published December 1, 2020.
Math Subject Classifications: 34B40, 35B05.
Key Words: Sublinear equation; radial solution; exterior domain.
Show me the PDF file (371 KB),
TEX file for this article.

Joseph A. Iaia
Department of Mathematics
University of North Texas, P.O. Box 311430
Denton, TX 762035017, USA
email: iaia@unt.edu

Return to the EJDE web page