Ground state solutions for generalized quasilinear Schrödinger equations without (AR) condition
Ground state solutions for generalized quasilinear Schrödinger equations without (AR) condition
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DOI：
10.1016/j.jmaa.2017.07.042
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发表时间：
2017-12
影响因子：
1.3
通讯作者：
Yinbin Deng;Wentao Huang
中科院分区：
文献类型：
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作者：
Yinbin Deng;Wentao Huang
本文研究了广义拟线性薛定谔方程− div（g2（u）<$u）+ g（u）g′（u）|u| 2+ V（x）u= h（x，u），x∈ R N，其中N≥ 3，g：R→ R+是一个偶可微函数，满足lim t→+∞ <$g（t）t α− 1= β> 0，其中α≥ 1; h（x，t）是一个给定的函数，在无穷远处的行为类似于t 2 α− 1，它不满足（A R）条件。结合变量变换和Jeanjean在[16]中发展的单调方法，我们得到了该问题正基态解的存在性。
In this paper, we study the following generalized quasilinear Schrödinger equations− div (g 2 (u)∇ u)+ g (u) g′(u)|∇ u| 2+ V (x) u= h (x, u), x∈ R N, where N≥ 3, g: R→ R+ is an even differentiable function satisfying lim t→+∞ g (t) t α− 1= β> 0 for some α≥ 1; h (x, t) is a given function behaving like t 2 α− 1 at infinity, which does not satisfy the (A R) 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.