  In this paper we are going to show the existence of a nontrivial solution to
the following model problem, \begin{equation*} \left\{\begin{array}{lll}
-\Delta (u) = 2uln(1+u^2)+\frac{|u|^2}{1+u^2}2u+u(sin(u)-cos(u)) \mbox{a.e. on
} \Omega \frac{\partial u}{\partial \eta} = 0 {a.e. on} \partial \Omega.
\end{array} \right. \end{equation*} As one can see the right hand side is
superlinear. But we can not use an Ambrosetti-Rabinowitz condition in order to
obtain that the corresponding energy functional satisfies (PS) condition.
However, it follows that the energy functional satisfies the Cerami (PS)
condition.
