Wenjing Chen, Jianfu Yang
Abstract:
Let
be a compact, connected, orientable,
Riemannian
-manifold of class
with Riemannian metric
.
We study the
existence of solutions to the equation
on this Riemannian manifold. Here
,
and
are continuous functions. We show that the shape
of
and
affects the number of solutions,
and then prove the existence of multiple solutions.
Submitted September 15, 2009. Published October 9, 2009.
Math Subject Classifications: 35J20, 35J61, 58J05.
Key Words: Multiple Solutions; Semilinear elliptic equation;
Riemannian manifold; Ljusternik-Schnirelmann category.
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Wenjing Chen Department of Mathematics, Jiangxi Normal University Nanchang, Jiangxi, 330022, China email: wjchen1102@yahoo.com.cn |
Jianfu Yang Department of Mathematics, Jiangxi Normal University Nanchang, Jiangxi, 330022, China email: jfyang_2000@yahoo.com |
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