Abstract:
In this article, we study the existence of infinitely many
solutions for the boundary–value problem
\begin{gather*}
-\Delta_\gamma u+a(x)u=f(x,u) \quad \text{in}\ \ \Omega, \qquad
u=0 \quad\text{on}\ \ \partial\Omega,
\end{gather*}
where
$\Omega$
is a bounded domain with smooth boundary in
$\mathbb{R}^N$ ($N \ge 2$)
and
$\Delta_{\gamma}$
is a subelliptic operator of the form
$$
\Delta_\gamma: =\sum\limits_{j=1}^{N}\partial_{x_j} \big(\gamma_j^2 \partial_{x_j} \big),
\qquad \partial_{x_j}:
=\frac{\partial }{\partial x_{j}},\quad \gamma = (\gamma_1, \gamma_2, \dots, \gamma_N).
$$
Our main tools are the local linking and the symmetric mountain pass theorem in
critical point theory.
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