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This paper is mainly concerned with the existence of ground statesign-changing solutions for a class of second order quasilinear ellipticequations in bounded domains which derived from nonlinear optics models.Combining a non-Nehari manifold method due to Tang and Cheng [31] and aquantitative deformation lemma with Miranda theorem, we obtain that the problemhas at least one ground state sign-changing solution with two precise nodaldomains. 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 MaximumPrinciple, we reach the conclusion that the energy of the ground statesign-changing solutions is strictly larger than twice that of the ground statesolutions.

Existence of ground state sign-changing solutions for a class of quasilinear scalar field equations originating from nonlinear optics