期刊论文

The existence of ground state solutions for generalized quasilinear Schrodinger equations

中文

中国科学.数学

1674-7216

2019

49

2

109-124

10.1360/N012018-00007

国家自然科学基金(批准号:11771170)资助项目.

本校为第一机构

本文旨在研究如下的广义拟线性Schr?dinger方程-div（g2（u）▽u）+g（u）g′（u）|▽u|2+V （x）u=h（u）, x∈RN,其中N≥3, g:R→R+是一个可微的偶函数且存在α≥1使得limt→+∞g（t）/tα-1=β> 0; h:R→[0,+∞)是一个非线性函数且包含情形:h（t）=|t|p-2t （2

In this paper, we study the following generalized quasilinear Schrodinger equations where N > 3, g: R → R + is an even differential function satisfying lim t → + ∞ g(t) tα - 1 = β > 0 for some α > 1; h: R → [0, + ∞ ) is a nonlinear function covering the case: h(t) = | t | p - 2 t (2 < p < α2 ∗ ); the potential V (x): R N → R is positive. Combining the change of variables and the variational argument, we prove the existence of a ...