Gregory S. Spradlin
Abstract:
We study the differential equation
,
where
is a double-well potential with minima at
and
as
.
It is proven that under certain additional assumptions on
,
there exists a heteroclinic solution
to the differential
equation with
as
and
as
.
The assumptions allow
to change sign for arbitrarily large values of
,
and do not restrict the decay rate of
as
.
Submitted May 21, 2009. Published September 23, 2010.
Math Subject Classifications: 34B40, 34C37.
Key Words: Heteroclinic; non-autonomous equation;
bounded solution; variational methods.
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Gregory S. Spradlin Department of Mathematics, Embry-Riddle University Daytona Beach, Florida 32114-3900, USA email: spradlig@erau.edu |
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