Electron. J. Diff. Eqns.,
Vol. 2005(2005), No. 05, pp. 1-20.
Multiplicity of symmetric solutions for a nonlinear eigenvalue
problem in
Daniela Visetti
Abstract:
In this paper, we study the nonlinear eigenvalue field equation

where
is a function from
to
with
,
is a positive parameter and
.
We find a multiplicity of solutions, symmetric with
respect to an action of the orthogonal group
:
For any
we prove the existence of finitely many
pairs
solutions for
sufficiently small,
where
is
symmetric and has topological charge
.
The multiplicity of our solutions can be as large as desired,
provided that the singular point of
and
are
chosen accordingly.
Submitted October 22, 2004. Published January 2, 2005.
Math Subject Classifications: 35Q55, 45C05.
Key Words: Nonlinear Schrodinger equations; nonlinear eigenvalue problems.
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Daniela Visetti
Dipartimento di Matematica Applicata
"U. Dini", Università degli studi di Pisa
via Bonanno Pisano 25/B, 56126 Pisa, Italy
email: visetti@mail.dm.unipi.it |
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