  In this paper we are going to show the existence of a nontrivial solution to
the following model problem,
  $\{\begin{array}{lll} - \Delta (u) =
2uln(1+u^2)+\frac{|u|^2}{1+u^2}2u+usin(u) {a.e. on} \Omega
  \frac{\partial u}{\partial \eta} = 0 {a.e. on} \partial \Omega. \end{array}
\}$
  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.
