Abstract
In this article, we study the existence of solutions for the Dirac system
{
D
u
=
∂
H
∂
v
(
x
,
u
,
v
)
on
M
,
D
v
=
∂
H
∂
u
(
x
,
u
,
v
)
on
M
,
\left\{\begin{aligned} \displaystyle Du&\displaystyle=\frac{\partial H}{% \partial v}(x,u,v)\quad\text{on }M,\\ \displaystyle Dv&\displaystyle=\frac{\partial H}{\partial u}(x,u,v)\quad\text{% on }M,\end{aligned}\right.
where M is an m-dimensional compact Riemannian spin manifold,
u
,
v
∈
C
∞
(
M
,
Σ
M
)
{u,v\in C^{\infty}(M,\Sigma M)}
are spinors, D is the Dirac operator on M, and the fiber preserving map
H
:
Σ
M
⊕
Σ
M
→
ℝ
{H:\Sigma M\oplus\Sigma M\rightarrow\mathbb{R}}
is a real-valued superquadratic function of class
C
1
{C^{1}}
with subcritical growth rates. Two existence results of nontrivial solutions are obtained via Galerkin-type approximations and linking arguments.