Electron. J. Differential Equations,
Vol. 2018 (2018), No. 178, pp. 114.
Positive solution curves of an infinite semipositone problem
Rajendran Dhanya
Abstract:
In this article we consider the infinite semipositone problem
in
,
a smooth bounded domain in
,
and u=0 on
,
where
and
,
.
Using stability analysis we prove the existence of a connected branch
of maximal solutions emanating from infinity. Under certain additional
hypothesis on the extremal solution at
we prove a version
of CrandallRabinowitz bifurcation theorem which provides a multiplicity
result for
.
Submitted May 3, 2018. Published November 1, 2018.
Math Subject Classifications: 35J25, 35J61, 35J75.
Key Words: Semipositone problems; topological methods; bifurcation theory.
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Rajendran Dhanya
School of Mathematics and Computer Science
Indian Institute of Technology
Goa 403401, India
email: dhanya.tr@gmail.com

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