-Laplacian semipositone equations
Abstract
We study positive
solutions to classes of boundary value problems of the form
in
on
, where
denotes the
-Laplacian operator defined by
;
,
is a parameter,
is a bounded domain in
;
with
of class
and connected (if
, we assume that
is a bounded open interval), and
for some
(semipositone problems). In particular, we first study the case when
where
is a parameter and
is a
function such that
,
for
and
for
. We establish positive constants
and
such that the above equation has a positive solution when
and
. Next we study the case when
(logistic equation with constant yield harvesting) where
and
is a
function that is allowed to be negative near the boundary of
. Here
is a
function satisfying
for
,
, and
. We establish a positive constant
such that the above equation has a positive solution when
Our proofs are based on subsuper solution techniques.
-Laplacian and constant yield harvesting. Abstract and Applied Analysis 2004,2004(9):723–727. 10.1155/S1085337504311097