  This paper is mainly concerned with the existence of ground state
sign-changing solutions for a class of second order quasilinear elliptic
equations in bounded domains which derived from nonlinear optics models.
Combining a non-Nehari manifold method due to Tang and Cheng [31] and a
quantitative deformation lemma with Miranda theorem, we obtain that the problem
has at least one ground state sign-changing solution with two precise nodal
domains. We also obtain that any weak solution of the problem has
$C^{1,\sigma}$-regularity for some $\sigma\in(0,1)$. With the help of Maximum
Principle, we reach the conclusion that the energy of the ground state
sign-changing solutions is strictly larger than twice that of the ground state
solutions.
