Existence of ground state sign-changing solutions for a class of generalized quasilinear Schrödinger-Maxwell system in R3

In this paper, we study the existence of ground state sign-changing solutions for the following generalized quasilinear Schrödinger-Maxwell system −div(g2(u)∇u)+g(u)g′(u)|∇u|2+V(x)u+μϕG(u)g(u)=K(x)f(u),x∈R3,−Δϕ=G2(u),x∈R3,where g∈C1(R,R+), V(x) and K(x) are positive continuous functions and μ is a positive parameter. By making a change of variable as u=G−1(v)andG(u)=∫0ug(t)dt,we obtain one ground state sign-changing solution vμ=G−1(uμ) by using some new analytical skills and non-Nehari manifold method. Furthermore, the energy of vμ=G−1(uμ) is strictly larger than twice that of the ground state solutions of Nehari-type. We also establish the convergence property of vμ=G−1(uμ) as the parameter μ↘0. Our results improve and generalize some results obtained by Chen and Tang (2016), Zhu et al. (2016).