In this talk, we investigate the existence of infinitely many non-constant weak solutions to the quasilinear elliptic equation
\[ -\text{div}(A(x,u)\nabla u) + \frac{1}{2} D_u A(x,u)\nabla u \cdot \nabla u = g(x,u) - \lambda u, \quad u\in H^1(\Omega), \]
for every \( \lambda \in \mathbb{R} \), where \( \Omega \) is a bounded domain with a Lipschitz continuous boundary.

Our approach is variational; however, the associated energy functional is differentiable only along directions \( v \in H^1(\Omega) \cap L^\infty(\Omega) \).

We discuss the notion of weak slope and the critical point theory for continuous functionals, and we apply these concepts to our problem to establish the existence of multiple solutions.