Abstract
We consider equations of the form
with Neumann boundary conditions. The key early reference
is by Angenent, Mallet-Paret and Peletier (1987), who found all stable
equilibrium solutions for a class of function
which are cubic in
, with
for large
. In joint work with S.B. Ai we study
the ``Duffing'' case
, and find a large class
of unstable equilibria, including solutions with multiple internal layers.
We also study the ode satisfied by the steady states as a nonlinear
oscillator, and obtain some chaos results which do not treat
as
a small parameter.
In the case of the Neumann problem for small
we are able to
obtain the Morse index of the new solutions. Further, we consider the
bifurcation of solutions as a function of
, and we anticipate
that near the initial bifurcation point it will be possible to apply
techniques of Fiedler and Rochas to determine the global attractor.
TUESDAY, October 31, 2000
Time: 1:30 P.M.
Location: PPB 300