Eun Kyoung Lee, Ratnasingham Shivaji, Jinglong Ye
Abstract:
We discuss the existence of positive solutions to
in
, with
on the boundary, where
is a positive parameter,
is a bounded domain with smooth boundary
is the Laplacian operator, and
is a continuous function. We first
discuss the cases when
(positone),
and
(semipositone). In particular, we will review the existence of
non-negative strict subsolutions. Along with these subsolutions and
appropriate assumptions on
for
(which will lead to
large supersolutions) we discuss the existence of positive
solutions. Finally, we obtain new results on the case of infinite
semipositone problems
().
Published April 15, 2009.
Math Subject Classifications: 35J25.
Key Words: Positone; semipositone; infinite semipositone;
sub-super solutions.
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Eun Kyoung Lee Department of Mathematics and Statistics, Center for Computational Sciences Mississippi State University, Mississippi State, MS 39762, USA email: el165@msstate.edu | |
Ratnasingham Shivaji Department of Mathematics and Statistics, Center for Computational Sciences Mississippi State University, Mississippi State, MS 39762, USA email: shivaji@ra.msstate.edu | |
Jinglong Ye Department of Mathematics and Statistics, Mississippi State University Mississippi State, MS 39762, USA email: jy79@msstate.edu |
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