Electron. J. Differential Equations,
Vol. 2019 (2019), No. 49, pp. 132.
Regularity of the lower positive branch for singular elliptic bifurcation problems
Tomas Godoy, Alfredo Guerin
Abstract:
We consider the problem
where
is a bounded domain in
,
,
, and
.
It is known that, under suitable assumptions on f, there exists
such that this problem has at least one weak solution in
if and only if
;
and that, for
,
at least two such solutions exist. Under additional hypothesis on a
and f, we prove regularity properties of the branch formed by the minimal
weak solutions of the above problem. As a byproduct of the method used,
we obtain the uniqueness of the positive solution when
.
Submitted August 7, 2018. Published April 12, 2019.
Math Subject Classifications: 35J75, 35D30, 35J20.
Key Words: Singular elliptic problems; positive solutions; bifurcation problems;
implicit function theorem; sub and super solutions.
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Tomas Godoy
FaMAF, Universidad Nacional de Córdoba
(5000) Córdoba, Argentina
email: godoy@mate.uncor.edu


Alfredo Guerin
FaMAF, Universidad Nacional de Córdoba
(5000) Córdoba, Argentina
email: guerin.alfredojose@gmail.com

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