Abstract:
This paper focuses on the following scalar field equation
\begin{equation*}
\begin{cases}
-\Delta u=f(u)&\text{in }\Omega,\\
u=0&\text{on }\partial\Omega,
\end{cases}
\end{equation*}
where
$\Omega=\mathbb{R}^k\times
D$,
$k\geq2$
and
$D$
is a bounded domain in
$\mathbb{R}^\ell$
with
$\ell\geq1$.
By using the variational method, we extend the results of Byeon and Tanaka in [6]
and prove, in the zero mass case, the existence of a positive axially symmetric
solution under suitable growth conditions on
$f$.
Keywords:nonlinear elliptic equations, striplike domains, zero mass case.
