@article{Hu2022, 
author = {Die Hu and Peng Jin and Xianhua Tang},
title = {The existence results for a class of generalized quasilinear Schrödinger equation with nonlocal term},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {5},
pages = {1973-1998},
keywords = {ground state solution, nonlocal term, Berestycki-Lions conditions, quasilinear Schrödinger equation},
url = {https://www.sciopen.com/article/10.3934/era.2022100},
doi = {10.3934/era.2022100},
abstract = {In this paper, we discuss the generalized quasilinear Schrödinger equation with nonlocal term:         −div(g2(u)∇u)+g(u)g′(u)|∇u|2+V(x)u=(|x|−μ∗F(u))f(u),x∈RN,(P)where  N≥3,  μ∈(0,N),  g∈C1(R,R+),  V∈C1(RN,R) and  f∈C(R,R). Under some "Berestycki-Lions type conditions" on the nonlinearity  f which are almost necessary, we prove that problem  (P) has a nontrivial solution  u¯∈H1(RN) such that  v¯=G(u¯) is a ground state solution of the following problem         −Δv+V(x)G−1(v)g(G−1(v))=(|x|−μ∗F(G−1(v)))f(G−1(v)),x∈RN,(P¯)where  G(t):=∫0tg(s)ds. We also give a minimax characterization for the ground state solution  v¯.}
}