Bryan P. Rynne
Abstract:
We prove that the set of nontrivial solutions
consists of a
curve of positive solutions in
,
with a parametrisation of the form
,
where
is a
function defined on
,
and
is a suitable weighted eigenvalue of the
-Laplacian
(
may be finite or
),
and
satisfies
We also show that for each
the solution
is globally asymptotically stable,
with respect to positive solutions
(in a suitable sense).
Submitted August 13, 2009. Published April 28, 2010.
Math Subject Classifications: 34B15.
Key Words: Ordinary differential equations; p-Laplacian;
nonlinear boundary value problems; positive solutions;
stability.
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Bryan P. Rynne Department of Mathematics and the Maxwell Institute for Mathematical Sciences Heriot-Watt University Edinburgh EH14 4AS, Scotland email: bryan@ma.hw.ac.uk |
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