In this work, we use variational methods to prove the existence of heteroclinic and saddle-type solutions for a class quasilinear elliptic equations of the form [Formula: see text] where [Formula: see text] is a N-function, [Formula: see text] is a periodic positive function and [Formula: see text] is modeled on the Ginzburg–Landau potential. In particular, our main result includes the case of the potential [Formula: see text], which reduces to the classical double well Ginzburg–Landau potential when [Formula: see text], that is, when we are working with the Laplacian operator.

The main goal of the present paper is to prove the existence of saddle-type solutions for the following class of quasilinear problems $$ -\Delta_{\Phi}u + V'(u)=0\quad \text{in }\mathbb{R}^2, $$% where $$ \Delta_{\Phi}u=\text{div}(\phi(|\nabla u|)\nabla u), $$% $\Phi\colon \mathbb{R}\rightarrow [0,+\infty)$ is an N-function and the potential $V$ satisfies some technical condition and we have as an example $ V(t)=\Phi(|t^2-1|)$.