The author deals with problems of the form \[ -\text{div}(a(x)\nabla u(x))= f(x,u)\quad \text{in }\Omega,\qquad {\partial u\over\partial n}= 0\quad \text{on }\partial\Omega,\tag{1} \] where \(\Omega\) is a bounded domain in \(\mathbb{R}^N\) with a \(C^1\) boundary \(\partial\Omega\), \(f(\cdot,\cdot)\) is a Carathéodory function and \(a(\cdot)\) is a positive weight on \(\Omega\). Under natural assumptions on the data of (1) the author provides two existence result for (1). To this end, the author uses a variational approach.