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

Abstract

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.