Ground state solutions for generalized quasilinear Schrödinger equations without (AR) condition

In this paper, we study the following generalized quasilinear Schrödinger equations−div(g2(u)∇u)+g(u)g′(u)|∇u|2+V(x)u=h(x,u),x∈RN, where N≥3,g:R→R+ is an even differentiable function satisfying limt→+∞⁡g(t)tα−1=β>0 for some α≥1; h(x,t) is a given function behaving like t2α−1 at infinity, which does not satisfy the (AR) condition. Combining the change of variables and the monotone method developed by Jeanjean in [16], we obtain the existence of positive ground state solutions for the given problem.