Electron. J. Diff. Equ.,
Vol. 2014 (2014), No. 207, pp. 129.
Multiple solutions to asymmetric semilinear elliptic problems via Morse theory
Leandro Recova, Adolfo Rumbos
Abstract:
In this article we study the existence of solutions to the problem
where
is a smooth bounded domain in
and
is a differentiable
function with g(x,0)=0 for all
.
By using minimax methods
and Morse theory, we prove the existence of at least three nontrivial
solutions for the case in which an asymmetric condition on the nonlinearity
g is assumed. The first two nontrivial solutions are obtained by
employing a cutoff technique used by Chang et al in [9].
For the existence of the third nontrivial solution, first we compute the
critical group at infinity of the associated functional by using a technique
used by Liu and Shaoping in [19]. The final result is obtained by
using a standard argument involving the Morse relation.
Submitted February 28, 2014. Published October 7, 2014.
Math Subject Classifications: 35J20.
Key Words: Morse theory; critical groups, local linking.
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Leandro L. Recova
Institute of Mathematical Sciences
Claremont Graduate University
Claremont, California 91711, USA
email: leandro.recova@cgu.edu


Adolfo J. Rumbos
Department of Mathematics, Pomona College
Claremont, California 91711, USA
email: arumbos@pomona.edu

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