Electron. J. Diff. Eqns., Vol. 1994(1994), No. 04, pp. 1-10.
V. Anuradha, S. Dickens, & R. Shivaji
Abstract:
We study solutions to the boundary value problems
where
,
is a bounded region in
;
with smooth boundary
,
,
uniformly in
, thus allowing for both positone as well as
semipositone structure, we discuss the existence of at least
three solutions for given
where
is the
subject
to the above boundary conditions.
In particular, one of the solutions we obtain has non-zero
positive part, while another has non-zero negative part.
We also discuss the existence of three solutions where one of
them is positive, while another is negative, for
near
, and for
large when
small.
Submitted January 23, 1994. Published July 8, 1994.
Math Subject Classification: 35J65.
Key Words: Elliptic boundary value problems, semipositone.
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V. Anuradha Department of Mathematics and Statistics University of Arkansas at Little Rock Little Rock, AR 72204-1099, USA | |
S. Dickens Department of Mathematics and Statistics Mississippi State University Mississippi State, MS 39762, USA | |
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R. Shivaji Department of Mathematics and Statistics Mississippi State University Mississippi State, MS 39762, USA e-mail: shivaji@math.msstate.edu |
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