The quasilinear elliptic variational equation \[ -\sum^n_{i,j=1}{\partial\over\partial x_j}\Biggl(a_{ij}(x,u){\partial u\over\partial x_i}\Biggr)+{1\over 2}\sum^n_{i,j=1}{\partial a_{ij}\over\partial u}(x,u){\partial u\over\partial x_i}{\partial u\over\partial x_j}=g(x,u)\quad\text{in }\Omega,\;u|_{\partial\Omega}=0 \] is shown to have infinitely many distinct weak solutions, if one assumes among other things: \(\Omega\subset\mathbb{R}^n\) is a bounded domain, the principal part is uniformly elliptic, even in \(u\), and satisfies some sign condition with respect to \(u\). The nonlinear lower order term is odd with respect to \(u\), superlinear and grows subcritically: \(|g(x,u)|\leq a+b|u|^p\) with \(1